costa concordia

SCHRIFTENREIHE SCHIFFBAU

Philipp Russell

The Sinking Sequence of M.V. Costa Concordia

A-44 | November 2013

Institute ofShip Design and Ship SafetyProf. Dr.-Ing. Stefan Kruger

Masters Thesis

The Sinking Sequence ofM.V. Costa Concordia

Philipp RussellRegistration Number 20837662

First Examiner:

Prof. Dr.-Ing. Stefan Kruger

Second Examiner:

Prof. Dr.-Ing. Moustafa Abdel-Maksoud

Hamburg, November 3, 2013

Declaration of Authorship

I hereby declare and confirm that this thesis and the work presented in it havebeen generated by me as the result of my own original research and that I havenot made use of any other sources than those stated in here.

(Place, Date) (Philipp Russell)

Contents

Contents

List of Figures III

List of Tables VI

Nomenclature VII

1 Introduction 1

2 Theory 22.1 Flow Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.1.1 Small Openings . . . . . . . . . . . . . . . . . . . . . . . . . 22.1.2 Large Openings . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Flooding Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2.1 Flux Integration . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.2 Pressure Propagation . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Grounding Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Accident 93.1 Description of the Ship . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 Summary of the Accident . . . . . . . . . . . . . . . . . . . . . . . 93.3 Timeline of Events . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Model 144.1 Hydrostatic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.2 Loading Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.3 Compartment Model . . . . . . . . . . . . . . . . . . . . . . . . . . 164.4 Opening Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.5 Watertight Doors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5 Results 275.1 Reference Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.1.1 Flooding Progression . . . . . . . . . . . . . . . . . . . . . . 275.1.2 Influence of the Different Compartments . . . . . . . . . . . 315.1.3 Final Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 37

5.2 Study of Influences . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.2.1 Rock Moment . . . . . . . . . . . . . . . . . . . . . . . . . . 385.2.2 Wind Moment . . . . . . . . . . . . . . . . . . . . . . . . . . 395.2.3 Stabiliser Moment . . . . . . . . . . . . . . . . . . . . . . . 435.2.4 Watertight Door 6 . . . . . . . . . . . . . . . . . . . . . . . 455.2.5 Watertight Door 9 . . . . . . . . . . . . . . . . . . . . . . . 475.2.6 Watertight Door 10 . . . . . . . . . . . . . . . . . . . . . . . 50

Institute of Ship Designand Ship SafetyProf. Dr.-Ing. Stefan Kruger

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Contents

5.2.7 Watertight Door 24 . . . . . . . . . . . . . . . . . . . . . . . 525.3 Most Likely Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.3.2 Influence of the Damaged Compartments . . . . . . . . . . . 585.3.3 Heel Change to Starboard . . . . . . . . . . . . . . . . . . . 645.3.4 Influence of the Undamaged Compartments . . . . . . . . . 675.3.5 Progressive Flooding of Deck 0 . . . . . . . . . . . . . . . . 695.3.6 Second Grounding . . . . . . . . . . . . . . . . . . . . . . . 74

5.4 Grounding Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.5 Hypothetical Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.5.1 Sinking at Sea . . . . . . . . . . . . . . . . . . . . . . . . . . 775.5.2 No Leak in Watertight Door 24 . . . . . . . . . . . . . . . . 795.5.3 All Watertight Doors Closed . . . . . . . . . . . . . . . . . . 80

6 Conclusion 82

References 86


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List of Figures

List of Figures

2.1 Flow through small openings . . . . . . . . . . . . . . . . . . . . . . 32.2 Flow through large openings . . . . . . . . . . . . . . . . . . . . . . 32.3 Integration stripe for large openings . . . . . . . . . . . . . . . . . . 42.4 Flooding graph of M.V. Costa Concordias initial damage . . . 52.5 Simplified subdivision model and openings of M.V. Costa Con-

cordias initial damage, sections of Deck A and on the Centreline . 62.6 Predictor-corrector scheme for = 0.5 . . . . . . . . . . . . . . . . 73.1 M.V. Costa Concordia . . . . . . . . . . . . . . . . . . . . . . . 93.2 Course of M.V. Costa Concordia . . . . . . . . . . . . . . . . . 103.3 M.V. Costa Concordia in her final position . . . . . . . . . . . 114.1 Hydrostatic model of M.V. Costa Concordia . . . . . . . . . . 144.2 Righting lever curve of M.V. Costa Concordia before the accident 164.3 Bulkhead plan of M.V. Costa Concordia . . . . . . . . . . . . . 174.4 Upper deck plan of sister ship . . . . . . . . . . . . . . . . . . . . . 184.5 Lower deck plan of sister ship . . . . . . . . . . . . . . . . . . . . . 194.6 Real leak and opening model, port side . . . . . . . . . . . . . . . . 214.7 Opening model of M.V. Costa Concordia . . . . . . . . . . . . 214.8 Watertight doors on Deck C, aft . . . . . . . . . . . . . . . . . . . . 224.9 Watertight doors on Deck C, midship . . . . . . . . . . . . . . . . . 224.10 Watertight doors on Deck C, forward . . . . . . . . . . . . . . . . . 234.11 Watertight doors on Deck B, forward . . . . . . . . . . . . . . . . . 234.12 Watertight doors on Deck A, aft . . . . . . . . . . . . . . . . . . . . 234.13 Watertight doors on Deck A, midship . . . . . . . . . . . . . . . . . 244.14 Watertight doors on Deck A, forward . . . . . . . . . . . . . . . . . 245.1 Floating position development in the reference case . . . . . . . . . 275.2 Damage zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.3 Volume fluxes into the compartments above the double bottom in

the reference case . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.4 Volume fluxes into the compartments in the double bottom in the

reference case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.5 Escape trunk on Deck C in Compartment 4 . . . . . . . . . . . . . 305.6 Deck A in Compartment 4 . . . . . . . . . . . . . . . . . . . . . . . 315.7 Water volumes in the rooms in Compartment 4 in the reference case 325.8 Heeling moments of the rooms in Compartment 4 in the reference

case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325.9 Water volumes in the rooms in Compartment 5 in the reference case 335.10 Heeling moments of the rooms in Compartment 5 in the reference

case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.11 Water volumes in the rooms in Compartment 6 in the reference case 34


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List of Figures

5.12 Heeling moments of the rooms in Compartment 6 in the referencecase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.13 Water volumes in the rooms in Compartment 7 in the reference case 355.14 Heeling moments of the rooms in Compartment 7 in the reference

case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.15 Water volumes in the rooms in Compartment 8 in the reference case 365.16 Heeling moments of the rooms in Compartment 8 in the reference

case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365.17 Righting lever curve at the equilibrium in the reference case . . . . 375.18 Fire door at frame 44 in the reference case viewed from aft . . . . . 375.19 Rock stuck in the leak . . . . . . . . . . . . . . . . . . . . . . . . . 385.20 Floating position development with rock moment . . . . . . . . . . 395.21 Lateral area of M.V. Costa Concordia . . . . . . . . . . . . . . 405.22 Floating position development with wind from starboard . . . . . . 415.23 Floating position development with wind from port . . . . . . . . . 415.24 AIS track of M.V. Costa Concordia . . . . . . . . . . . . . . . 425.25 Ship speed and stabiliser moment according to AIS track . . . . . . 435.26 Floating position development with stabiliser . . . . . . . . . . . . . 445.27 Position of portside stabiliser after the accident . . . . . . . . . . . 445.28 Watertight Door 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.29 Volume flux through Watertight Door 6 . . . . . . . . . . . . . . . . 455.30 Water volumes in Compartments 7 and 8 with activation of WTD 6 465.31 Heeling moments of Compartments 7 and 8 with activation of WTD 6 465.32 Floating position development with activation of WTD 6 . . . . . . 475.33 Watertight Door 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.34 Volume flux through Watertight Door 9 . . . . . . . . . . . . . . . . 485.35 Water volumes in Compartments 4 and 5 with activation of WTD 9 485.36 Heeling moments of Compartments 4 and 5 with activation of WTD 9 495.37 Floating position development with activation of WTD 9 . . . . . . 495.38 Watertight Door 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.39 Volume flux through Watertight Door 10 . . . . . . . . . . . . . . . 505.40 Water volumes in Compartments 3 and 4 with activation of WTD 10 515.41 Heeling moments of Compartments 3 and 4 with activation of WTD

10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.42 Floating position development with activation of WTD 10 . . . . . 525.43 Watertight Door 24 . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.44 Volume flux through Watertight Door 24 . . . . . . . . . . . . . . . 535.45 Water volumes in Compartments 3 and 4 with activation of WTD 24 535.46 Heeling moments of Compartments 3 and 4 with activation of WTD

24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545.47 Floating position development with activation of WTD 24 . . . . . 545.48 Leaking types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56


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List of Figures

5.49 M.V. Costa Concordia at 21:48 UTC . . . . . . . . . . . . . . . 575.50 Floating position at 21:48 UTC in the most likely scenario . . . . . 575.51 Floating position development in the most likely scenario . . . . . . 585.52 Main switchboard rooms at the time of the blackout . . . . . . . . . 585.53 Water volumes in Compartment 6 in the most likely scenario . . . . 595.54 Heeling moments of Compartment 6 in the most likely scenario . . . 595.55 Water volumes in Compartment 7 in the most likely scenario . . . . 605.56 Heeling moments of Compartment 7 in the most likely scenario . . . 605.57 Water volumes in Compartment 5 in the most likely scenario . . . . 615.58 Heeling moments of Compartment 5 in the most likely scenario . . . 615.59 Volume flux through Watertight Door 24 in the most likely scenario 625.60 Water volumes in Compartment 4 in the most likely scenario . . . . 625.61 Heeling moments of Compartment 4 in the most likely scenario . . . 635.62 Water volumes in Compartment 8 in the most likely scenario . . . . 635.63 Heeling moments of Compartment 8 in the most likely scenario . . . 645.64 Deck A in Compartment 3 . . . . . . . . . . . . . . . . . . . . . . . 655.65 Garbage plant on Deck 0 . . . . . . . . . . . . . . . . . . . . . . . . 665.66 Water volumes in Compartment 3 in the most likely scenario . . . . 675.67 Heeling moments of Compartment 3 in the most likely scenario . . . 675.68 Water volumes in Compartment 2 in the most likely scenario . . . . 685.69 Heeling moments of Compartment 2 in the most likely scenario . . . 685.70 Rooms on the freeboard deck (Deck 0) . . . . . . . . . . . . . . . . 695.71 Volume fluxes due to progressive flooding . . . . . . . . . . . . . . . 705.72 Water volumes on deck 0 in the most likely scenario, part 1 . . . . . 715.73 Heeling moments of deck 0 in the most likely scenario, part 1 . . . . 715.74 Water volumes on deck 0 in the most likely scenario, part 2 . . . . . 725.75 Heeling moments of deck 0 in the most likely scenario, part 2 . . . . 725.76 Water volumes on deck 0 in the most likely scenario, part 3 . . . . . 735.77 Heeling moments of deck 0 in the most likely scenario, part 3 . . . . 735.78 M.V. Costa Concordia at 21:55 UTC . . . . . . . . . . . . . . . 745.79 Floating position at 21:55 UTC in the most likely scenario . . . . . 745.80 Floating position development while grounding . . . . . . . . . . . . 755.81 Final floating position with a seabed stiffness of 50 t/m . . . . . . . 765.82 Final floating position with a seabed stiffness of 5 t/m . . . . . . . 765.83 Floating position development while sinking at sea . . . . . . . . . . 775.84 Critical openings while sinking at sea . . . . . . . . . . . . . . . . . 775.85 Immersion of Deck 4 while sinking at sea . . . . . . . . . . . . . . . 785.86 Floating position development without leak in Watertight Door 24 . 795.87 Floating position development with all watertight doors closed . . . 805.88 Floating position at 21:55 UTC with all watertight doors closed . . 81


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List of Tables

List of Tables

3.1 Main particulars of M.V. Costa Concordia . . . . . . . . . . . . 93.2 Important events . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.3 Flooded compartments . . . . . . . . . . . . . . . . . . . . . . . . . 134.1 Comparison of the cross-curves of stability . . . . . . . . . . . . . . 144.2 Loading condition of M.V. Costa Concordia before sinking . . . 154.3 Opening types and collapsing pressure heights . . . . . . . . . . . . 204.4 Watertight door activity outside the damaged compartments . . . . 254.5 Watertight door activity inside the damaged compartments . . . . . 254.6 Failure of watertight doors . . . . . . . . . . . . . . . . . . . . . . . 265.1 Data used for the wind heeling moment . . . . . . . . . . . . . . . . 405.2 Water exchanged through watertight doors . . . . . . . . . . . . . . 555.3 Leaking values of different openings . . . . . . . . . . . . . . . . . . 56


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Nomenclature

Nomenclature

AIS Automatic Identification SystemBSU Bundesstelle fur Seeunfalluntersuchung (Federal Bureau

of Maritime Casualty Investigation)DB Double BottomEU European Union

FLOODSTAND Integrated Flooding Control and Standard for Stabilityand Crises Management

MCIB Marine Casualties Investigative BodyMFZ Main Fire Zone

MODU Mobile Offshore Drilling UnitSOLAS International Convention for the Safety of Life at Sea

UPS Uninterruptible Power SupplyUTC Coordinated Universal TimeVDR Voyage Data RecorderWTD Watertight Door

Latin Letters

dV Volume difference [m3]dz Pressure height difference [m]dz Earth-fixed clearance to seabed [m]x Earth-fixed coordinate [m]R Rotation matrix []x Ship-fixed coordinate [m]A Cross section area [m2]B Moulded breath [m]C Seabed stiffness [N/m]Cd Discharge coefficient []CL Lift coefficient []D Depth [m]F Force [N ]g Gravitational constant [m/s2]H Water depth [m]LOA Length over all [m]LPP Length between perpendiculars [m]M Moment [Nm]p Air pressure [Pa]p Position vector [m]


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Nomenclature

Q Volume flux [m3/s]R Righting lever of stabiliser [m]s Integration variable lying in the opening plane [m]T Draught [m]t Time [s]

TCB Transverse Centre of Buoyancy [m]u Water velocity [m/s]V Volume [m3]v Ship speed [kn]

VCB Vertical Centre of Buoyancy [m]VS Service speed [kn]w Cross-curve of stability [m]z Water level [m]

Greek Letters

Pressure difference independent of water level [m] Relaxation factor [] Heeling angle [] Dissipative energy term [m2/s2] Density of water [kg/m3] Trim angle []

Subscripts

c Corrector-related termsp Predictor-related terms


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1 INTRODUCTION

1 Introduction

The M.V. Costa Concordia sank in the early morning of January 14, 2012 nearthe island of Giglio in the Mediterranean Sea. The night before she had hit anunderwater rock when performing a tight high-speed turn very close to the shore.As a result of this collision she drifted powerless near to the harbour of Giglio.Here she grounded a second time and evacuation procedures were started. Thelist gradually increased until she finally capsized and came to rest on the rocks inshallow waters.

Thirty-two the 4229 persons on board lost their lives during the flooding andcapsizing of the ship. Because twelve of the victims were Germans, the FederalBureau of Maritime Casualty Investigation (BSU) is obligated to conduct an inves-tigation in addition to the official one performed by the Italian Marine CasualtiesInvestigative Body (MCIB) [10]. In the scope of this investigation the BSU cooper-ates with the Institute of Ship Design and Ship Safety at the Hamburg Universityof Technology.

The accident will be simulated by means of a progressive flooding simulation.Using this simulation the sequence of events is to be reproduced in order to gaininsight into the possible failure modes. The influence of opening and closing water-tight doors is of particular interest and will be determined in detail. In addition,the role of the second ground contact near the harbour as well as the influence ofwind and other possible external moments shall be investigated.


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2 THEORY

2 Theory

The sinking simulation program used to investigate the accident has been devel-oped at the Institute of Ship Design and Ship Safety at the Hamburg Universityof Technology [3]. It utilises a quasi-static approach, which is able to determinethe flooding of a ship and the resulting floating position in the time domain. Theship is subdivided into compartments with corresponding openings. The volumefluxes through these openings are calculated using the incompressible, rotational-and viscous-free Bernoulli equation. At each time step the new filling level of eachcompartment is computed so that the resulting floating position can be determinedby hydrostatic means. Air compression as well as conditions for the openings liketime-dependent activations or collapsing pressure heights can be taken into ac-count. The following is a short abstract of the underlying physical model used forthe simulation, further details can be found in [3].

2.1 Flow Calculation

According to the Bernoulli theorem the energy along a streamline is constant andconsisting of pressure, kinetic and potential parts. This holds for an irrotationaland stationary flow of an incompressible and inviscid fluid and can be formulatedas follows:

p

1

gdp+

u2

2g+ z

g= const. (2.1)

The first three terms in equation 2.1 describe the mentioned energy parts, whereasthe term allows for pressure losses to be modelled.

2.1.1 Small Openings

In the case of small openings, i.e. no change in cross section and velocity acrossthe opening, there are two relevant modes of flow. These are the free outflow asshown in figure 2.1 on the left side and the deeply submerged flow pictured onthe right of the same figure. Neglecting the dissipative term for now the pressureheight difference becomes

pa pbg

+u2a u2b

2g+ za zb ab

g= dz , (2.2)

wherein some terms can be neglected depending on the type of flow. The velocityat the opening is in each case given by

u =

2g dz . (2.3)The pressure losses are now considered by a discharge coefficient Cd

u = Cd

2g dz (2.4)



2 THEORY

reducing the flow velocity. This coefficient is semi-empirical and accounts for thecontraction of the flow as well as viscous effects. It visually depicts the ratio of theflow cross section behind the opening in relation to the opening area. For a normalopening it assumes a value of around 0.6. The resulting volume flux through theopening is then given by

dV

dt= Q = A u . (2.5)

pa pb

za

zb

a

bz0

pa pb

za

zb

a

b

z0

Figure 2.1: Flow through small openings [3]

2.1.2 Large Openings

In the case of large openings the flow velocity and the cross section area can differover the opening extension, leading to a more complex flux calculation. However,the two basic modes free outflow and deeply submerged flow can superpose anypossible flow situation, as shown in figure 2.2. For the deeply submerged partequation 2.2 can be used to determine the flow velocity.

(1)

h1

h2

za zb

(4)

h1

h2za

zb

(2)

h1

h2

za zb

(5)

h1

h2za zb

(3)

h1

h2

za

zb

(6)

h1

h2

za

zb

Figure 2.2: Flow through large openings [3]



2 THEORY

The volume flux of the free outflow part on the other hand demands an approachconsidering the position and form of the large opening. For this purpose theopening, which is in general a polygon stretching in any direction, is divided bystripes in z-direction. This way the velocity can be described in the earth-fixedz-direction, while the integration to obtain the volume flux is performed in s-direction, as shown in figure 2.3.

z

yh1

z0

z1

h2za

s

y

y1

y(s)

y0

s1s z

z0

z1

Figure 2.3: Integration stripe for large openings [3]

The shape function of the z-stripe is a linear variation of the form

y(s) = y0 + s y1 y0s1

, (2.6)

while the free outflow velocity can be determined through

u(s) =

2g za (z0 + sz s) +

with =pag

pbg

+u2a2g

and sz =z1 z0s1

.

(2.7)

The term contains the pressure differences independent of z, while sz containsinformation about the orientation of the opening [3]. To get the volume flux of thefree outflow part, the integration

Q =

A

u dA =

s

y

u(s) dy ds =

s10

u(s) y(s) ds (2.8)

needs to be performed. Solving the integral for equation 2.6 and 2.7 yields theanalytical solution for the volume flux through one stripe:

Q = 23sz

2g [y1 h

321 y0 h

320 +

2(y1 y0)5(z1 z0) (h

521 h

520 )

]with h1 = h(s1) = za z1 + and h0 = h(0) = za z0 +

(2.9)



2 THEORY

2.2 Flooding Process

The flooding paths of the ship are modelled using graph theory with the com-partments as nodes and directed edges representing the various openings. Anidentification number is assigned to all compartments ascending from keel to top,from bow to stern and from port to starboard. The direction of the edges joiningthe compartments is then defined positive if connecting ascending identificationnumbers. This direction is only a sign convention and does not have to representthe actual flooding direction.

An example of a flooding graph is shown in figure 2.4 for a simplified case ofthe initial damage of M.V. Costa Concordia. In the actual model there areseveral cases of multiple openings between compartments, especially to representthe damage, but these have been omitted here for simplification purposes. Thearrangement of the compartments and openings involved in this sample floodinggraph is demonstrated in figure 2.5. As is evident from these pictures, representingthe actual model with nodes and edges allows for a quicker identification of vitalopenings and neighbourhood relationships.

(1) Outside(2) WB.DB.10C

(3) WB.DB.11C (4) WB.DB.12C (5) VO.DB.6C

(9) Aft D/G PS (11) ElectricMotors

(12) RefrigerationCompressors

(8) Fwd D/G Stairs

(6) Fwd D/G PS

(7) Fwd D/G SB

(13) Switchboard PS

(14) Switchboard SB

(10) Aft D/G SB

1

2 3 4

6 7

11

12

8

5

9 10

13

1415

1617

Figure 2.4: Flooding graph of M.V. Costa Concordias initial damage



2 THEORY

x

z

Deck A

WB.DB.10CWB.DB.11CWB.DB.12CVO.DB.6C

Fwd D/G SBAft D/G SBElectric Motors

Refr. Compr.

Swbd. SB

. 1.2. 3. 4

. 7. 8

. 13. 14

.17

12

16

4 5 6 7 8Compartment

x

y

Centreline

567

9

131417

1011

15

16

Fwd D/G PS

Fwd D/G SB

Aft D/G PS

Aft D/G SB

Electric Motors

Swbd. PS

Swbd. SB

FwdD/GStrs.

Figure 2.5: Simplified subdivision model and openings of M.V. Costa Concor-dias initial damage, sections of Deck A and on the Centreline

2.2.1 Flux Integration

The overall flux to or from a certain compartment is formed by the sum of allthe fluxes through each opening to this compartment. By integrating the fluxover a set time interval the water volume transferred between the compartmentsis obtained:

dV (t) =

t2t1

Qo(t) dt (2.10)

Using this volume, the new water levels inside the compartments can be calculated.This calculation has to be done in an iterative way due to the arbitrary geometricstructure of the compartments and thus non-linear relationship between volumefilling and water level. Furthermore, the flux Qo(t) also depends non-linear onthe water level. To consider these non-linearities in the calculation, a weightedpredictor-corrector scheme is employed to determine the exchange of water volumebetween the compartments:

dVc = dt ( Qo(tp) + (1 ) Qo(t0)) , (2.11)



2 THEORY

dVc = dVp + (1 ) dV0 . (2.12)In there denotes the relaxation factor, which is set to 0.5. A relaxation factorstabilises an iteration for a given value below 1, as is the case here. The predictor-corrector scheme is then applied as visualised in figure 2.6.

fluxQ

(t)

time tt0 t1

Qo(t0)dV0 (2.)

dVp (4.)

dVc (5.)

Qo(t1)

dt

Figure 2.6: Predictor-corrector scheme for = 0.5 [3]

2.2.2 Pressure Propagation

In the case of several neighbouring compartments being totally flooded there isa non-linear coupling between these compartments because the calculation of thefluxes cannot be independently performed. Therefore some requirements need tobe met:

- The sum of all fluxes to and from a compartment has to be zero.

- Water flowing from partially full compartments must spread through the fullcompartment.

- The free variable to be determined is the pressure in the full compartment.

The resulting non-linear equation system is constructed using a sub-graph of therelated filled compartments. If for instance the compartment containing the port-side aft diesel generators is completely full of water, the governing equation yields:

Q = A6 g (z1 z9) + p1 p9

+ A10 g (z6 z9) + p6 p9

+ A11 g (z9 z11) + p9 p11

+ A14 g (z9 z10) + p9 p10

+ A15 g (z9 z13) + p9 p13 = f(p9) = 0 .

(2.13)

This non-linear equation can be solved with respect to the unknown pressure p9employing an iterative algorithm to answer the pressure propagation problem.



2 THEORY

2.3 Grounding Model

In the scope of a semi-submersible heavy lift ship accident the presented sinkingsimulation program has been enhanced to consider reaction forces due to grounding[4]. This will be important in the later phase of the M.V. Costa Concordiaevent.

The position and movement of a ship can be described in two basic coordinatesystems, a ship-fixed one with axes specified by Latin letters and an earth-fixedone with Greek letter axes. Both have their origin in the aft perpendicular onthe centreline, but the ship-fixed one is located at the keel and moves with theship, while the earth-fixed lies on the water surface and does not move. Eithercoordinate system is right-handed with x or positive in forward direction, y or positive to port and z or positive upwards. For hydrostatic purposes only threedegrees of freedom are relevant, namely the draught T , the trim angle (positiveif the bow is deeper submerged than the stern) and the heeling angle (positiveto starboard). Therefore the relation between the two coordinate systems can bedescribed using a rotation matrix R:

x = R x t (2.14)

= cos sin sin cos sin0 cos sin

sin sin cos cos cos

xyz

00T

(2.15)Forces and moments are added up within the earth-fixed system and the hydro-static equilibrium is then found in an iterative way. To consider the influence ofground contact, the seabed is represented by springs. At each time step everypoint of the hydrostatic model with the position vector p is checked for contactwith the seabed, positioned in a certain depth H. Using the third row vector r3 ofthe rotation matrix R,

dz = H r3 p + T (2.16)yields the earth-fixed distance dz between point and seabed. If this value is greaterthan zero, the seabed with the stiffness C exerts a grounding force of

F = C dz , (2.17)otherwise there is no force due to ground contact. This force additionally leads totrim moments M and heeling moments M, which can be determined using thefirst and second row vector of the matrix R:

M = F = F r1 x (2.18)M = F = F r2 x (2.19)

The forces and moments resulting from ground contact are then added to theexisting ones, so that they affect the equilibrium.



3 ACCIDENT

3 Accident

3.1 Description of the Ship

The M.V. Costa Concordia was built in 2004 by Fincantieri in Sestri Ponentefor the Italian cruise line Costa Crociere. Her main particulars are given in table3.1 and a picture of the vessel in undamaged condition is shown in figure 3.1.

Table 3.1: Main particulars of M.V. Costa Concordia [10]

Length over all LOA 290.20 mLength between perpendiculars LPP 247.70 mBreadth B 35.50 mDepth D 11.20 mSummer draught T 8.30 mService speed VS 19.60 kn

Figure 3.1: M.V. Costa Concordia (Source: Costa Crociere)

3.2 Summary of the Accident

Having left the port of Civitavecchia near Rome on the evening of January 13,2012 the ship was on her way to Savona in Northern Italy with 3206 passengers



3 ACCIDENT

and 1023 crew on board. En route she changed her planned course and headedfor Giglio at a speed of over 15 knots where she was to perform a tight starboardturn near the coast. In doing so she collided with the Scole Rocks below thewaterline on her port side, so that five watertight compartments were hit. Thesecontained amongst others the electric propulsion motors, all diesel generators aswell as the main switchboard. The initial list was to port due to the leak being onthat side and because of the heeling moment caused by the contact with the rocks,which stuck inside the vessel after the impact. After a while the flooding becamealmost symmetrical and the ship went upright again. Having been damaged incompartments vital for power generation, power distribution and propulsion, shewas soon adrift without electricity. Even though the emergency diesel generatorstarted up, it did not work reliable enough to provide power. Thus, emergencypower was supplied by UPS batteries. However, the steering gear did not functionand thrusters needed more than emergency power. So, due to wind and current thevessel was eventually moved north of Giglio harbour. There the forces of natureturned her around 180 degrees and pushed her in the direction of the island untilshe grounded a second time, as shown in figure 3.2.

Figure 3.2: Course of M.V. Costa Concordia [10]

At this time the evacuation procedures were started, while the heeling angle to



3 ACCIDENT

starboard continuously increased. In the early hours of the next morning, she hadfinally capsized and sunk onto the seabed approximately 25 metres deep. Thereshe had been laying in a position pictured in figure 3.3 until she was at last raisedon September 16, 2013.

Figure 3.3: M.V. Costa Concordia in her final position (Source: Getty Images)

3.3 Timeline of Events

To check the results of the sinking simulation against the real situation, a timelineof important events needs to be established. In this case, important refers toincidents relevant to the sinking process, which means ascertained progress of floodwater, actions inducing heeling moments and the development of the heeling angle.Therefore, occurrences concerning passenger safety and evacuation are omittedhere, although they are of course relevant for the investigation of the BSU. Aninteresting sociological study on the events during the accident has been performedat the Bielefeld University, which led to the release of vital VDR data by theItalian consumer protection organisation Codacons [2]. Times stated in this thesisare UTC, the local time at Giglio is UTC plus one hour. The running time inseconds serves to verify the relevant events during the sinking simulation, which isstarted at the time of the impact. Heeling angles are given positive to starboardand hence negative to port. The decks of M.V. Costa Concordia below thefreeboard deck, which is named Deck 0, are labelled C to A in ascending order



3 ACCIDENT

starting above the double bottom. The source of the information compiled intable 3.2 is the official investigation report from the Italian Marine CasualtiesInvestigative Body and VDR data available to the Institute of Ship Design andShip Safety through the BSU and the MCIB [10] [13] [14]. In addition, the BSUhas ordered a photogrammetric expertise from the Leibniz University Hannoveron the floating position at the time of dropping the starboard anchor, 21:48 UTC[16].

Table 3.2: Important events [10] [13] [14] [16]

UTC[hh:mm:ss]

t [s] Heel [] Event

20:45:07 0

3 ACCIDENT

the wind is now coming from the port side. Approximately 40 minutes past thecollision water reaches the freeboard deck, Deck 0, while it heels the ship almost10 degrees to starboard.

The starboard anchor is dropped one hour and a few minutes after the accidentafter several failed attempts. According to the photogrammetric evaluation theship has a starboard list of about 14 to 14.5 degrees at that time. This order ofmagnitude of the heeling angle is supported by the statement of a bridge officeraround the same time. The trim angle is determined to be 1.2 degrees, whichresults in a trim of 5.19 metres to the aft. There is of course some measuringinaccuracy so that the real angles may differ slightly. Nevertheless these valuesare the most reliable ones because they are not based on observations made by thecrew in a stressful situation. Thus, they will serve as a reference point.

One hour and ten minutes subsequent to the first grounding the vessel groundsa second time with the aft starboard side. At the same time the first lifeboats arelaunched, starting on the starboard side to reduce the list. The last heeling anglestated by the crew on the VDR is 25 to 30 degrees to starboard at 22:11:26 UTC.Almost three hours after taking the damage the vessel capsizes assuming a heelingangle of around 90 degrees as confirmed by a coastguard helicopter. From here onshe sinks completely and comes to rest on the rocks with a list of approximately70 degrees.

Table 3.3: Flooded compartments [10]

Compartment Contents Deck

4 Refrigeration compressors CCrew cabins A

5 Void space Double BottomElectric propulsion motors CSynchroconverters A

6 Water ballast tank Double BottomAft diesel generators CIncinerators CMain switchboard A

7 Water ballast tank Double BottomForward diesel generators CLube oil purifiers CEngine workshop A

8 Water ballast tank Double Bottom



4 MODEL

4 Model

4.1 Hydrostatic Model

Figure 4.1: Hydrostatic model of M.V. Costa Concordia

The hull form of the vessel is modelled up to and including Deck 11 and the funnelusing plans of M.V. Costa Concordia and an identical sister ship [12] [8]. Thisresults in the hydrostatic model shown in figure 4.1. The cross-curves of stability

w () = TCB cos () + VCB sin () (4.1)of this model are then checked against the ones of the loading computer, as pre-sented in table 4.1.

Table 4.1: Comparison of the cross-curves of stability [12]

Cross-curve Model [m] Loading computer [m] Relative deviation [%]

w (10) 3.299 3.295 0.1w (20) 6.584 6.556 0.4w (30) 9.583 9.552 0.3w (40) 11.835 11.786 0.4w (50) 13.243 13.095 1.0w (60) 14.363 14.325 0.3



4 MODEL

Differences in the given order of magnitude are to be expected because it is notpossible to reproduce the exact lines of the vessel using the given plans. Giventhis limitation, the quality of the model is considered to be acceptable for theintended purpose. In contrast to classical hydrostatics, where only the water- orweathertight part is used, the sinking simulation requires the whole hull includingthe superstructure.

4.2 Loading Condition

Table 4.2: Loading condition of M.V. Costa Concordia before sinking [12]

Shell plating factor 1.002 -Density of sea water 1.025 t/m3

Ships weight 54998.680 tLongitudinal centre of gravity 118.610 m.b.APTransverse centre of gravity -0.010 m.f.CLVertical centre of gravity (solid) 16.850 m.a.BLFree surface correction of V.C.G. 0.344 mVertical centre of gravity (corrected) 17.194 m.a.BLDraught at A.P (moulded) 7.901 mDraught at LBP/2 (moulded) 8.115 mDraught at F.P (moulded) 8.328 mTrim (pos. fwd) 0.427 mHeel (pos. stbd) 0.320 Deg.Volume (incl. shell plating) 53657.242 m3

Longitudinal centre of buoyancy 118.632 m.b.APTransverse centre of buoyancy -0.081 m.f.CLVertical centre of buoyancy 4.388 m.a.BLArea of waterline 7988.557 m2

Longitudinal centre of waterline 111.632 m.b.APTransverse centre of waterline -0.072 m.f.CLMetacentric height 1.711 m

The loading condition of M.V. Costa Concordia at her departure from Civi-tavecchia is given in table 4.2. It is pretty close to the design state with a slightforward trim and almost no heel. The associated righting lever curve is depictedin figure 4.2. All of the relevant intact stability criteria are fulfilled, including theweather criterion, passenger heeling and turning circle moment. The righting levercurve itself with the high initial metacentric height is typical for a cruise ship tocomply with comfort requirements.



4 MODEL

-1

-0.5

0

0.5

1

1.5

2

0 10 20 30 40 50 60 70

Rig

htin

g le

ver [m

]

Heeling angle [deg]

LC PRIOR DAMAGE starboard side

GZ [m]Requ. or Max. h: 0.971 m

Progfl. or Max.: 56.945 Deg.

GM at Equilib. : 1.711 mArea under GZ [mrad]

Figure 4.2: Righting lever curve of M.V. Costa Concordia before the accident

4.3 Compartment Model

Using the bulkhead plan of M.V. Costa Concordia in figure 4.3 and the deckplan of an identical sister ship in figures 4.4 and 4.5, the compartmentation of theship is modelled. This is done in the confinements of the hydrostatic model, whichmeans up to and including Deck 11, because this is the last continuous deck. Allrooms are assumed to be fully ventilated, so that air compression is neglected.The fire-proof A-class walls and decks are expected to prevent the spread of water,thus they form the main compartment boundaries. Furthermore, certain B-classbarriers like cabin walls also determine compartments, but are modelled with largeopenings as described further down. Lifts, staircases and large spaces are modelledas one compartment with the appropriate vertical extension. The permeabilityof the compartments is set to SOLAS standards, that is 0.6 for stores, 0.85 formachinery spaces and 0.95 for every other space [5]. Though certain simplificationsconcerning the compartment model need to be made, the whole ship still consistsof 642 compartments.



4 MODEL

Figure 4.3: Bulkhead plan of M.V. Costa Concordia [12]



4 MODEL

Figure 4.4: Upper deck plan of sister ship [8]



4 MODEL

Figure 4.5: Lower deck plan of sister ship [8]



4 MODEL

4.4 Opening Model

Compartments are connected to each other and to the sea via one or more openings.The state of the openings is derived from the given plans; a door normally closedis modelled as closed and vice versa. Each of these openings needs a name, theidentification numbers of the compartments to connect, coordinates of the openingcentre and spatial extensions in the relevant directions. Furthermore, values forthe semi-empirical discharge coefficient and the collapsing pressure heights arerequired. The allowable heights of water pressing on an closed opening before itcollapses depend on the type of the opening and are given in table 4.3. Thesevalues are in line with classification society requirements and results of the EUproject FLOODSTAND [15].

Table 4.3: Opening types and collapsing pressure heights [15] [12]

Opening type Collapsing pressure height [m]

Non-weathertight opening 0.5Elevator door 1.0Fire door 2.0Cold store door 3.5Weathertight opening 5.0Splashtight door 8.0Window 20.0Watertight door 50.0

As described above, the discharge coefficient for most of the openings is set to 0.6.However, there are some exceptions to this rule. The first one applies to groups ofsmall similar openings like cabin windows, which are treated as one large openingto reduce the modelling effort. The volume flux Q through the simplified openingshall be the same as through the n original ones with their individual dischargecoefficient Cd,0 = 0.6 [3]:

Q = Cd,new Alarge u = n Cd,0 Asmall u (4.2)

Therefore, it holds

Cd,new = n Cd,0 AsmallAlarge

(4.3)

for the modified discharge coefficient, which is always lesser than 0.6 because thelarge opening also contains the areas between the small openings.

In the case of modelling the aforementioned cabin walls, an almost similar ap-proach is chosen, with the cabin walls as large and the cabin doors as small open-ings. In addition, a probability factor of p = 0.5 is introduced because it is unknown



4 MODEL

which cabin doors are actually open:

Cd,new = p n Cd,0 AsmallAlarge

(4.4)

The last exception in terms of discharge coefficients is the leak itself. It is modelledwith eleven openings using the dimensions given in the official investigation reportas illustrated in figure 4.6. For most of these openings the discharge coefficientis assumed to be 0.6, only in the case of the rearmost leak it is altered to 0.2 toaccount for the obstruction caused by the rock.

x

z

Deck 0

Deck A

Deck B

Deck C

WB.DB.10CWB.DB.11CWB.DB.12CVO.DB.6C

Fwd D/G PSAft D/G PSElectric MotorsRefr. Compr.

Swbd. PS

FwdD/GStrs.

4 5 6 7 8

Figure 4.6: Real leak and opening model, port side [10]

Even with the mentioned simplifications, there are in total 1580 openings definedto connect the compartments, which are presented in figure 4.7.

Figure 4.7: Opening model of M.V. Costa Concordia



4 MODEL

4.5 Watertight Doors

According to the SOLAS rules in force at the date of keel laying, the subdivi-sion factor, which is dependent on ship type and length, specifies that the M.V.Costa Concordia has to withstand the flooding of two contiguous watertightcompartments. Therefore, the ship is subdivided into 19 compartments by wa-tertight bulkheads reaching from the keel of the ship to the freeboard deck Deck0. To allow the crew to pass bulkheads in the watertight part without the detourvia the freeboard deck, the M.V. Costa Concordia is fitted with 25 watertightdoors. These are positioned on the three decks Deck C, Deck B and Deck A at thevarious bulkheads, as shown in figures 4.8 to 4.14 with the damage zone markedin blue.

11 10 9

8 7

Figure 4.8: Watertight doors on Deck C, aft [12]

6 5

4 3 2

1

Figure 4.9: Watertight doors on Deck C, midship [12]



4 MODEL

1

Figure 4.10: Watertight doors on Deck C, forward [12]

1312

Figure 4.11: Watertight doors on Deck B, forward [12]

25 24

Figure 4.12: Watertight doors on Deck A, aft [12]



4 MODEL

23 22 21 20 1918

Figure 4.13: Watertight doors on Deck A, midship [12]

19 1817

16 15 14

Figure 4.14: Watertight doors on Deck A, forward [12]

Watertight doors are normally only open during harbour activities. They canbe opened at sea to perform works near them but shall be closed immediatelyand their activation shall be noted in the log. With the approval of the flag stateadministration some watertight doors may be kept open at sea if deemed necessary.In the case of M.V. Costa Concordia these exceptions are Watertight Doors7, 8, 12, 13 and 24.

Any activation of a watertight door is also registered in the VDR. For the minutesafter the accident these activation times from the VDR are given in tables 4.4 and4.5 regarding the watertight doors outside and inside the damage zone, respectively.



4 MODEL

Table 4.4: Watertight door activity outside the damaged compartments [14]

UTC [hh:mm:ss] t [s] WTD 5 WTD 11 WTD 12 WTD 13

20:45:07 0 closed closed open open20:45:29 22 opening closed open open20:45:43 36 closing closed open open20:45:52 45 closed closed open open20:46:27 80 closed closed open closing20:46:29 82 closed closed open closed20:47:11 124 closed closed closing closed20:47:15 128 closed closed closed closed20:47:51 164 closed opening closed closed20:48:01 174 closed closing closed closed20:48:02 175 closed closed closed closed

Table 4.5: Watertight door activity inside the damaged compartments [14]

UTC [hh:mm:ss] t [s] WTD 6 WTD 9 WTD 10 WTD 24

20:45:07 0 closed closed closed closed20:45:18 11 closed opening closed closed20:45:29 22 closed closing closed closed20:45:39 32 closed closed closed closed20:45:48 41 closed closed opening closed20:45:50 43 opening closed opening closed20:46:03 56 closing closed open closed20:46:08 61 closed closed open closed20:46:13 66 closed closed closing closed20:46:27 80 closed closed closed closed20:49:52 285 closed closed closed opening20:50:12 305 closed closed closed closing20:50:15 308 closed closed closed closed

The only doors open at the time of the accident are 12 and 13, which are locatedfar from the leak near the laundry on Deck B. These two doors are closed almostimmediately by order of the master. Other doors in the damage zone facilitate theescape of some crew members and are thus opened and closed after the collisionwith the rocks. Watertight doors should not be used as an escape route becauseevery watertight compartment is fitted with vertical escape trunks for this purpose.In the case of M.V. Costa Concordia however the latter may not have been inreach due to the entering water.



4 MODEL

It has to be noted that the status open or closed is only updated with somedelay, while the activation timesopeningandclosingare exact times. Therefore,in the sinking simulation the opening/closing time of the watertight doors is setto the minimum of 20 seconds as required by SOLAS and started at these exacttimes [5]. If a door is closed again before it is fully opened, the maximum level ofopenness is derived from the ratio of passed time to opening time. It also has tobe said that some of the door activations take place after the blackout. However,the Italian investigators are sure that the operation of the doors is independentof the main electrical supply, therefore the watertight door activity is modelled asdescribed above [11].

After some time into the events, the status of several watertight doors changesto fault, shown in table 4.6. This is most likely due to water reaching the sensorson or near the door. To what extent the mechanical damage of the door is relatedto the electrical failure of the sensors remains unknown. Only in the case ofWatertight Door 24 a leak has been reported by witnesses but without detailsregarding time or leak size [10].

Table 4.6: Failure of watertight doors [14]

UTC [hh:mm:ss] t [s] Heel [] Event

22:01:10 963 10 Failure of Watertight Door 922:32:26 2839 >10 Failure of Watertight Door 822:33:16 2889 >10 Failure of Watertight Doors 7 and 2522:35:29 3022 >10 Failure of Watertight Doors 10 and 11

Furthermore, there are some splashtight doors on the freeboard deck, whose statusis also monitored on the VDR, but these are not opened or closed during theaccident. They are thus modelled according to their opening status and with anappropriate collapsing pressure height as stated in table 4.3.



5 RESULTS

5 Results

Using the presented sinking simulation and the computation model, there are sev-eral cases to be calculated. Each of the different influence factors will be consideredindependently at first and compared to a reference case. These influence factorsinclude different induced heeling moments, the activation of watertight doors aswell as leaking through various key openings. In the end a most likely scenariowith the combined influence factors will be presented. Based on this most likelyscenario several hypothetical scenarios will be discussed. Finally, the necessaryconclusions will be drawn.

5.1 Reference Case

5.1.1 Flooding Progression

The first case to be evaluated will serve to demonstrate the initial phase of theflooding and as a reference case. For this purpose the model as described is usedaccording to the given plans [12] [8]. In these plans every door has a designatedopening status, which is used for the model. Neither the time-dependent activationof watertight doors nor external effects are considered. Furthermore, any closedopening does not leak until the collapsing pressure height is reached.

The calculation of this reference case yields the evolution of the floating positionshown in figure 5.1 starting at the time of the collision.

-15

-10

-5

0

5

10

15

20:45 20:50 20:55 21:00 21:05 21:10 21:15 21:20 21:25

Drau

ght [

m],

Trim

[m],

Heel

[deg

]

UTC [H:M]

DraughtTrim

Heeling angle

Figure 5.1: Floating position development in the reference case

The water entering through the rupture caused by the rocks immediately heels the



5 RESULTS

ship around 14 degrees to port and increases the draught by over 2 metres. Over thenext eight minutes the flooding becomes symmetrical and the heeling changes tostarboard. Twenty minutes into the accident, after the flooding of the last possiblecompartments, the vessel reaches an equilibrium at about 12 metres draught at theaft perpendicular, an aft trim of nearly five metres and approximately 0.5 degreeheeling angle to starboard.

4 5 6 7 8Compartment

Deck C

Double Bottom

Void 7 pt

Aft Aux.

Void 7 sb

Refr. Comp.Ele. Mot. Aft D/G pt

Aft D/G sb

Incinerators

Fwd D/G Strs

Fwd D/G pt

Fwd D/G sb

LO Purifiers

Sewage Room

Void 6 Wat. Ball. 12 Wat. Ball. 11 Wat. Ball. 10

Figure 5.2: Damage zone [12]

After the collision with the rocks water enters into five compartments. This isillustrated in figure 5.2, where the damaged compartments are indicated in red,while the leaks are shown in blue. Compartments 5 and 6 containing the aft dieselengines and the electric motors fill up very fast due to the large and unobstructedleaks. As is illustrated in figure 5.3, the volume fluxes reach 10000 and more cubicmetres per minute. In contrast, Compartment 4 with the refrigeration compressorsas well as Compartments 7 and 8 including the forward diesel engines take moretime to flood. In the case of Compartment 4 this is because of the rock blockingthe still large leak, so that the volume fluxes into the compartment reach only 2000cubic metres per minute. The leaks in Compartments 7 and 8 are relatively smalland thus take only a few hundred cubic metres per minute on board, but over alonger time.



5 RESULTS

0

2000

4000

6000

8000

10000

12000

20:45 20:47 20:49 20:51 20:53 20:55 20:57 20:59 21:01 21:03 21:05

Volu

me

flux

[m3 /

min

]

UTC [H:M]

Forward Diesel Engines StairsAft Diesel Engines port 1Aft Diesel Engines port 2

Electric Motors 1Electric Motors 2

Refrigeration Compressors

Figure 5.3: Volume fluxes into the compartments above the double bottom in thereference case

The double bottom compartments show the same behaviour as the ones above thedouble bottom, as is to be seen in figure 5.4. Void Space 6 and Water Ballast Tank12 in Compartments 5 and 6 suffer from larger leaks and become flooded within aminute. Water Ballast Tanks 10 and 11 in compartments 8 and 7 are only affectedby a minor scratch in the hull, so that it takes more time to fill them up.

0

500

1000

1500

2000

2500

20:45 20:47 20:49 20:51 20:53 20:55 20:57 20:59 21:01 21:03 21:05

Volu

me

flux

[m3 /

min

]

UTC [H:M]

Water Ballast DB 10CWater Ballast DB 11CWater Ballast DB 12C

Void Space DB 6C 1Void Space DB 6C 2

Figure 5.4: Volume fluxes into the compartments in the double bottom in the ref-erence case



5 RESULTS

As the rooms directly affected by the leak become flooded, the door to the escapetrunk in the Refrigeration Compressors Room marked in figure 5.5 breaks afterthe collapsing pressure height of two metres has been reached.

Void 7 pt

Aft Aux. Room

Void 7 sb

Refrigeration Compressors Electric Motors

Aft D/G pt

Aft D/G sb

Incinerators

Figure 5.5: Escape trunk on Deck C in Compartment 4 [12]

Via the upper exit of this escape trunk marked red in figure 5.6 the water is enabledto enter the crew spaces on Deck A and spread across the cabins. Apart from thecabins there are some openings of compartments critical for the upflooding processalso located in this area. These are the doors of the two aft Service Lifts marked



5 RESULTS

in yellow in the same figure as well as two doors leading to the staircase of mainfire zones 1 and 2 marked blue in there.

Workshops pt

Workshops ct

Aft Staircase

Workshops sb

Buffet Preparation

Deck A Crew 12

Deck A Crew 11

Figure 5.6: Deck A in Compartment 4 [12]

5.1.2 Influence of the Different Compartments

The amount of flood water in the various rooms of Compartment 4 in this referencecase is indicated in figure 5.7 and the resulting heeling moment in figure 5.8,wherein positive heeling moments mean a heel to port.



5 RESULTS

0

500

1000

1500

2000

2500

3000

20:45 20:47 20:49 20:51 20:53 20:55 20:57 20:59 21:01 21:03 21:05

Volu

me

[m3 ]

UTC [H:M]

Refrigeration CompressorsDeck A Crew 11.1Deck A Crew 11.2Deck A Crew 11.3Deck A Crew 11.4Deck A Crew 11.5

Deck A Crew 11 CorridorStaircase MFZ 1+2

Sum

Figure 5.7: Water volumes in the rooms in Compartment 4 in the reference case

-2000

-1000

0

1000

2000

3000

4000

5000

6000

7000

8000

20:45 20:47 20:49 20:51 20:53 20:55 20:57 20:59 21:01 21:03 21:05

Heeli

ng m

omen

t [tm

]

UTC [H:M]

Refrigeration CompressorsDeck A Crew 11.1Deck A Crew 11.2Deck A Crew 11.3Deck A Crew 11.4Deck A Crew 11.5

Deck A Crew 11 CorridorStaircase MFZ 1+2

Sum

Figure 5.8: Heeling moments of the rooms in Compartment 4 in the reference case

The most decisive room due to its size is the Refrigeration Compressors Room,which is flooded first and which determines the heeling moment of this compart-ment in the first minutes after the accident. As soon as the water reaches Deck A,the outmost crew cabins (11.1) become relevant for the heel, but the entire watervolume in the crew spaces only adds up to around half of that in the RefrigerationCompressors Room.



5 RESULTS

The situation in Compartment 5 shown in figures 5.9 and 5.10 is different becauseit mainly consists of the Electric Motors Room, which dominates the effect of thiscompartment. Furthermore, this room also fills up very quick due to the largeleak not being obstructed by a rock. The other rooms in this compartment areeither symmetrical and full in the end or cancel each other out in terms of heelingmoment.

0

500

1000

1500

2000

2500

3000

3500

20:45 20:47 20:49 20:51 20:53 20:55 20:57 20:59 21:01 21:03 21:05

Volu

me

[m3 ]

UTC [H:M]

Void Space DB 6CElectric Motors

Synchroconverter Room portSynchroconverter Room starboard

Sum


-2000

0

2000

4000

6000

8000

10000

12000

20:45 20:47 20:49 20:51 20:53 20:55 20:57 20:59 21:01 21:03 21:05

Heeli

ng m

omen

t [tm

]

UTC [H:M]

Void Space DB 6CElectric Motors

Synchroconverter Room portSynchroconverter Room starboard

Sum




5 RESULTS

Compartment 6 is the biggest one of the damaged compartments and has thusthe greatest influence, as is to be seen in figures 5.11 and 5.12. It is transverselysubdivided into the two engine rooms and the Incinerators Room, which flood oneafter another from port to starboard. The blackout of the ship about two minutesafter the collision coincides well with the flooding of the second Main SwitchboardRoom on the starboard side of Deck A.

0

1000

2000

3000

4000

5000

6000

20:45 20:47 20:49 20:51 20:53 20:55 20:57 20:59 21:01 21:03 21:05

Volu

me

[m3 ]

UTC [H:M]

Water Ballast DB 12CAft Diesel Engines port

Aft Diesel Engines starboardIncinerators Room

Main Switchboard Room portMain Switchboard Room starboard

Sum


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0

5000

10000

15000

20000

25000

20:45 20:47 20:49 20:51 20:53 20:55 20:57 20:59 21:01 21:03 21:05

Heeli

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omen

t [tm

]

UTC [H:M]

Water Ballast DB 12CAft Diesel Engines port

Aft Diesel Engines starboardIncinerators Room

Main Switchboard Room portMain Switchboard Room starboard

Sum




5 RESULTS

It takes much more time for the water to enter Compartment 7 because it isonly affected by a small leak in the Engine Staircase and a mere scratch in thedouble bottom, which is illustrated in figures 5.13 and 5.14. The time to flood isamplified by the fact that the Engine Staircase is only a small compartment, whichis only connected via small openings to the portside Forward Engine Room. Asa consequence the qualitative development of the heeling moment differs from theother compartments with no visible peak.

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[m3 ]

UTC [H:M]

Water Ballast DB 11CForward Diesel Engines port

Forward Diesel Engines StairsForward Diesel Engines starboard

Lube Oil Purifiers RoomEngine Workshop

Sum


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0

5000

10000

15000

20:45 20:47 20:49 20:51 20:53 20:55 20:57 20:59 21:01 21:03 21:05

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]

UTC [H:M]

Water Ballast DB 11CForward Diesel Engines port

Forward Diesel Engines StairsForward Diesel Engines starboard

Lube Oil Purifiers RoomEngine Workshop

Sum




5 RESULTS

The flooding of Compartment 8, which is only damaged in the double bottom,points out the significance of intermediate stages of flooding. In the beginningthere is only little water with an extensive lever arm and in the end there is lots ofwater with almost no lever arm. The most critical situation however is given as perfigures 5.15 and 5.16 by about 50 per cent filling. Especially in the case of morecomplex room geometries, a time domain flooding simulation provides valuableinsight into these intermediate stages in contrast to a pure hydrostatic analysis.

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[m3 ]

UTC [H:M]

Water Ballast DB 10C


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Water Ballast DB 10C




5 RESULTS

5.1.3 Final Equilibrium

The righting lever curve of the vessel in the equilibrium reached in the referencecase is given in figure 5.17. Due to the special hydrostatic model used by thesinking simulation, which also incorporates the non-weathertight part of the ship,the righting levers are positive even for very high angles of heel. Furthermore, thewater volumes in the compartments remain fixed for the calculation of the rightinglevers, although in reality they would change with increasing heeling angle.

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Righ

ting

Leve

r [m

]

Heeling Angle [deg]

GZ GM

Figure 5.17: Righting lever curve at the equilibrium in the reference case

There is water pressing on several non-watertight openings on the freeboard deck,but these are assumed not to leak in the reference case. Therefore, they preventprogressive flooding via the freeboard deck. The most critical of these openingsdue to its size and location is the double fire door on Deck 0 at frame 44, which isoriented to the stern of the ship and leads into the aft corridor as marked in figure5.18. The influence of leaking through these openings is investigated further down.

Figure 5.18: Fire door at frame 44 in the reference case viewed from aft



5 RESULTS

5.2 Study of Influences

5.2.1 Rock Moment

Figure 5.19: Rock stuck in the leak [12]

During the collision one rock was ripped of the cliffs and stuck in the ship likepictured in figure 5.19. The rock has an assumed weight of 97 tonnes and anassumed density of 2.7 t/m3, which results in a submerged weight of around 60tonnes. With an estimated transverse centre of gravity of 10.7 metres measuredfrom the centre line, the rock applies a heeling moment of about 650 tm. This



5 RESULTS

is equivalent to a shift of the transverse centre of gravity of the vessel by 11.8millimetres to port.

To investigate the influence of the rock moment, another calculation is performedwith identical settings as in the reference case, but with the centre of gravity of thevessel shifted by the named value. The results are given and checked against thereference case in figure 5.20. The development of draught and trim is practicallythe same but the heeling angle evolution differs due to the rock being on the portside. Initially the influence of the rock moment is small compared to the thousandsof metre tonnes heeling moment applied by the flood water. But as soon as thecrew spaces in Compartment 4 on Deck A begin to flood after about four minutes,the rock moment is decisive and forces the final equilibrium on the port side.

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ght [

m],

Trim

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[deg

]

UTC [H:M]

Draught referenceTrim reference

Heeling angle referenceDraught with rock

Trim with rockHeeling angle with rock

Figure 5.20: Floating position development with rock moment

5.2.2 Wind Moment

To consider the influence of heeling moments due to wind, the lateral area of theship shown in figure 5.21 has been entered into the computation model.

The wind velocity and density of air result in a certain pressure, which affectsthe lateral area to yield a lateral force. It is assumed that this force is acting on thecentroid of the lateral area above the waterline. The wind force is then equalisedby a hydrodynamic force applied at the centroid of the lateral area below thewaterline so that these two forces form a heeling moment. The heeling momentalso depends on a form-specific drag coefficient as well as on the heeling anglebecause lateral area and force application point are reduced with increasing angle.



5 RESULTS

Figure 5.21: Lateral area of M.V. Costa Concordia [12]

Table 5.1: Data used for the wind heeling moment [9]

Drag coefficient 1.200 -Density of air 1.225 kg/m3

Draught 8.115 mLateral area above waterline 9343.100 m2

Lateral area centroid above baseline 21.818 mWind velocity 10.000 knWind direction 22.500

All the relevant data for the wind heeling moment is given in table 5.1. The winditself is blowing from north-north-east at 18 knots, measured on a mountain nearGiglio at a height of over 600 metres [9]. Due to the boundary layer formed bythe wind over land and sea the wind velocity is lower in lesser heights. Accordingto the MODU Code design loads a wind velocity of 18 knots in over 256 metresheight is equivalent to 10 knots wind velocity at sea level, which is therefore usedhere [6].

The floating position development with 10 knots of wind from the starboardside is shown in figure 5.22, calculated with the same settings as in the referencecase. With the parameters given above, the wind moment is a little more thanhalf of the rock moment. Consequently, the draught and trim of the ship remainthe same as in the reference case but the heeling angle develops similar to the rockmoment case. Once again, the influence of the external moment begins to showafter four minutes, when the crew spaces in Compartment 4 on Deck A fill withwater. The final equilibrium however is now barely on the starboard side with anheeling angle of circa 0.05 degrees.



5 RESULTS

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Drau

ght [

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Trim

[m],

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[deg

]

UTC [H:M]


Heeling angle referenceDraught with wind from starboard

Trim with wind from starboardHeeling angle with wind from starboard

Figure 5.22: Floating position development with wind from starboard

If the wind blows from port with the same velocity, the calculation yields thefloating position development in figure 5.23. Again, the wind moment comes intoplay after 4 minutes but has little effect later on.

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ght [

m],

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[m],

Heel

[deg

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Heeling angle referenceDraught with wind from port

Trim with wind from portHeeling angle with wind from port

Figure 5.23: Floating position development with wind from port

In both of the above calculations the wind does hit the side of the vessel at an angleof 90 degrees. However, as the AIS track of the vessel in figure 5.24, this is notthe case in the real situation. Especially around the estimated time of the heeling



5 RESULTS

angle transition to starboard the wind blows almost from the front. Even duringthe rest of the time the relative angle between ship and wind seldom exceeds 45 de-grees. The wind velocity decreases with a trigonometric function depending on thedefinition of the angles, while the wind moment decreases with the wind velocitysquared. Furthermore, the heeling moment of the drift force caused by the currentsomewhat equalises the wind moment. Recognising the results of the calculationsperformed above and taking into account the aforementioned effects, it is thereforedecided to exclude the wind moment from further calculations. Nevertheless, thewind combined with the current and the rudder locked hard to starboard after theblackout is vital for the turn and the drift ashore, which may have prevented amuch more severe development of the accident.

10kn

ots

ofw

ind

Figure 5.24: AIS track of M.V. Costa Concordia [10]



5 RESULTS

5.2.3 Stabiliser Moment

As can be seen in several photos taken after the accident, the portside stabiliser ofthe vessel is in a position, which would give maximum lift to starboard. Therefore,the influence of the stabilisers is to be investigated as well. The heeling momentfor a pair of stabilisers is given by [1]:

MStabi = 2 2v2A CL R (5.1)

In there, denotes the density of sea water, v the speed of the vessel and A thearea of each stabiliser fin. The dimensions of one fin are estimated using photosand the bulkhead plan to 5.8 metres by 2.32 metres. CL is the lift coefficient of thestabiliser profile. It is set to 3 based on a conservative two-dimensional view andan angle of attack of approximately 30 degrees. R finally is the distance betweenthe centre of lift on the profile and the centre of the waterline, which gives thelever arm for the stabiliser moment. It amounts to half of the ships breadth plusa conservative estimation of half the stabilisers breadth.

Using the given formula with the ships speed taken from the AIS, which is shownin figure 5.25, this yields the heeling moment of the stabilisers in the same figure.

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Spee

d [k

n]

UTC [H:M]

Stabiliser momentShip speed

Figure 5.25: Ship speed and stabiliser moment according to AIS track [10]

It is currently unclear if the stabilisers were extended during the collision becausethe weather conditions were good. Due to the movement of the vessels stern toport before the contact with the rocks the stabilisers would not have been damagedby the first ground contact. In any case, they would have not started to act until acertain heeling angle was reached. Therefore, the stabiliser moment is modelled asshown in the picture with no heeling moment at start and maximum lift from the



5 RESULTS

first AIS time index after the collision onwards. With decreasing speed of coursethe heeling moment decreases as well up to a point where it practically vanishes.

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ght [

m],

Trim

[m],

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[deg

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UTC [H:M]


Heeling angle referenceDraught with stabiliser

Trim with stabiliserHeeling angle with stabiliser

Figure 5.26: Floating position development with stabiliser

Using the described time-dependent stabiliser moment, the floating position of thevessel develops as shown in figure 5.26 compared to the reference case. In thisfigure the only recognisable difference is even lower than in the case with 10 knotsof wind from port. It is thus very likely, that any efforts of the stabilisers to uprightthe ship would have been hindered by the wind blowing from starboard. In thisway, these two influences could have cancelled each other out during the initialphases of the flooding.

In the final position of the vessel shown in figure 5.27, the starboard stabiliseris certainly destroyed, so that the hydraulic pressure needed to operate the fins islost. Hence it could be possible, that the position of the portside stabiliser visiblein the photos is due to this pressure loss. Furthermore, it is unknown, to whatextent the stabilisers could actually be operated after the blackout. It is thereforedecided to exclude the stabiliser moment from any further calculations.

Figure 5.27: Position of portside stabiliser after the accident [10]



5 RESULTS

5.2.4 Watertight Door 6

According to the VDR data, four watertight doors in the damage zone have beenopened and closed after the accident, as presented in table 4.5. In the following,the influence of the opening and closing (hereafter denoted activation) of thesedoors shall be investigated individually for each door using the same settings as inthe reference case.

Figure 5.28: Watertight Door 6

The first door to be examined is Watertight Door 6 on Deck C marked in figure5.28, which connects the port Forward Engine Room in Compartment 7 with theSewage Room in Compartment 8. As can be seen in figure 5.29, this door is opened43 seconds after the accident to 65 per cent, reaches a maximum volume flux ofabout 250 cubic metres per minute and is again fully closed from 69 seconds on.

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Volu

me

flux

[m3 /

min

]

UTC [H:M:S]

Flux through WTD 6

Figure 5.29: Volume flux through Watertight Door 6

Approximately 55 cubic metres of water enter through Watertight Door 6 intothe Sewage Room, which is not much compared to the volumes in the rooms of



5 RESULTS

Compartment 7, which are presented in figure 5.30.

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Forward Diesel Engines portForward Diesel Engines Stairs

Forward Diesel Engines starboardLube Oil Purifiers Room

Engine WorkshopSewage Room

Figure 5.30: Water volumes in Compartments 7 and 8 with activation of WTD 6

Due to the layout of the Sewage Room the water spreads over the whole breadth ofthe ship. Consequently, even this little amount of water still leads to a significantheeling moment of approximately 750 metre tonnes, as shown in figure 5.31.

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Forward Diesel Engines portForward Diesel Engines Stairs

Forward Diesel Engines starboardLube Oil Purifiers Room

Engine WorkshopSewage Room

Figure 5.31: Heeling moments of Compartments 7 and 8 with activation of WTD6

The floating position development with the activation of Watertight Door 6 is



5 RESULTS

pictured in figure 5.32. Once again, the additional heeling moment is effectiveafter four minutes, when the crew spaces on Deck A flood. However, due to theextra flooded room the stability of the vessel is decreased and the heeling thereforechanges with a steep gradient to starboard after 14 minutes. The ship then comesto an equilibrium with about 1.2 degrees angle of heel.

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[m],

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[deg

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Heeling angle referenceDraught with WTD 6

Trim with WTD 6Heeling angle with WTD 6

Figure 5.32: Floating position development with activation of WTD 6



The next door under investigation is Watertight Door 9 marked in figure 5.33,leading from the Electric Motors Room in Compartment 5 to the RefrigerationCompressors Room in Compartment 4 on Deck C. These rooms are both affectedby large leaks, so no large influence of this door activation is to be expected. Again,



5 RESULTS

the same assumptions as in the reference case apply for the calculation of this dooractivation. The door is opened 11 seconds after the rock contact to 55 per cent.During this activation, the volume flux comes up to 430 cubic metres per minute,as indicated in figure 5.34, until the door is closed at 33 seconds into the accident.

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[m3 /

min

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Flux through WTD 9


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Electric Motors referenceRefrigeration Compressors reference

Deck A Crew 11.1 referenceDeck A Crew 11 Corridor reference

Electric Motors with WTD 9Refrigeration Compressors with WTD 9

Deck A Crew 11.1 with WTD 9Deck A Crew 11 Corridor with WTD 9


Figures 5.35 and 5.36 compare the reference case with the activation of WatertightDoor 9. There is not much difference between these two cases. The only effect



5 RESULTS

is a little accelerated filling of the Refrigeration Compressors Room because theopening of the door bypasses the leak in this room, which is obstructed by therock. This acceleration however is merely noticeable because there are only about80 cubic metres of water exchanged.

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Electric Motors referenceRefrigeration Compressors reference

Deck A Crew 11.1 referenceDeck A Crew 11 Corridor reference

Electric Motors with WTD 9Refrigeration Compressors with WTD 9

Deck A Crew 11.1 with WTD 9Deck A Crew 11 Corridor with WTD 9


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m],

Trim

[m],

Heel

[deg

]

UTC [H:M]


Heeling angle referenceDraught with WTD 9

Trim with WTD 9Heeling angle with WTD 9

Figure 5.37: Floating position development with activation of WTD 9

Because the local influence of the door activation is already small, the global



5 RESULTS

influence is even smaller, as figure 5.37 shows, so that the activation of WatertightDoor 9 could be excluded from the model. However, there may be more complexinteractions due to effects not considered in this simple evaluation of its influence.Therefore, Watertight Door 9 will be considered in further calculations.



Another door that has been opened after the accident is Watertight Door 10,which connects the Refrigeration Compressors Room in Compartment 4 to theAft Auxiliary Room in Compartment 3 on Deck C, as marked in figure 5.38. TheAft Auxiliary Room then leads to large void spaces on both sides of the ship.This door is fully opened 41 seconds after the collision and is again closed from 86seconds onwards. Figure 5.39 shows that during the 5 seconds it is fully open theflux reaches about 800 cubic metres per minute.

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[m3 /

min

]

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Flux through WTD 10




5 RESULTS

The total amount of water rushing through the door adds up to approximately350 cubic metres, as is to be seen in figure 5.40. This is again not much comparedto the other rooms involved, but it is sufficient to have the greatest influence of allwatertight doors on the heeling moments so far, which is shown in figure 5.41.

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Refrigeration CompressorsDeck A Crew 11.1

Deck A Crew 11 CorridorAft Auxiliary Room

Void Space 7 portVoid Space 7 starboard


-3000-2000-1000

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Refrigeration CompressorsDeck A Crew 11.1

Deck A Crew 11 CorridorAft Auxiliary Room

Void Space 7 portVoid Space 7 starboard


This influence becomes even clearer in the floating position development as per



5 RESULTS

figure 5.42. Due to the newly flooded compartment being positioned aft of thedamage zone, draught and trim are visibly increased compared to the referencecase. The ad

costa concordia

Documents

deck c

costa concordia144

sections of deck

deck b

opening model of

grounding model

progressive flooding

upper deck plan of sister