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SCHRIFTENREIHE SCHIFFBAU

Nicolas Rox

Examination of the intact stability and the seakeeping behaviour of container vessels within the ballast condition

Dezember 2010

DIPLOMARBEIT

für Herrn cand. arch. nav. Nicolas RoxMatr.-Nr. 25794

Examination of the intact stability and the seakeeping behaviour of container vessels within the ballast condition

The scope of this thesis is to examine, if the ballast condition of container vessels is supposed to be a seagoing condition or if there is an increased risk of accident in this case due to the design of this specific ship type.

For this reason Nicolas Rox is asked to examine the intact stability and the seakeeping behaviour of various sized container vessels within the ballast condition for situations that have led to accidents with this ship type as is known. The examination is supposed to be done based on computer models which exist at the Institute of Ship Design and Ship Safety at the Hamburg University of Technology, whereas the loading conditions should be according to the issued stability booklets.

Finally approaches to reduce the risk of accident shall be provided!

Beginn der Arbeit: 04. August 2010Abgabe der Arbeit: 03. Dezember 2010

Hamburg, 04. August 2010 ____________________ Prof. Dr.-Ing. S. Krüger

Postanschrift: Telefon: E-mail:Prof. Dr.-Ing. Stefan Krüger ++49 (40) 428 78 - 6105 [email protected]. für Entwerfen von Schiffen und Schiffssicherheit Fax: www.ssi.tu-harburg.deSchwarzenbergstraße 95, Gebäude C ++49 (40) 428 78 - 6139D - 21073 Hamburg

1st Examiner: Prof. Dr.-Ing. Stefan Krüger

2nd Examiner: Prof. Dr.-Ing. Moustafa Abdel-Maksoud

December 2010

I hereby declare and con�rm that this thesis is entirely the result of my own work. I did notutilise any other sources and appliances than those speci�ed in the bibliography.

Contents

List of Figures V

List of Tables VII

1 Introduction 1

1.1 Key data of the three examined accidents . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Accident of the CMS Chicago Express [1] . . . . . . . . . . . . . . . . 11.1.2 Accident of a 2468 TEU container vessel [2] . . . . . . . . . . . . . . . . 21.1.3 Accident of a 2500 TEU container vessel [3] . . . . . . . . . . . . . . . . 2

1.2 Following objectives for the diploma thesis . . . . . . . . . . . . . . . . . . . . . . 3

2 Theory 5

2.1 Description of the utilised seakeeping simulation method . . . . . . . . . . . . . 52.1.1 Linear strip method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1.1 Calculation model . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.1.2 Roll radius of inertia and roll period . . . . . . . . . . . . . . . . 62.1.1.3 Roll damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1.1.4 Calculation settings . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.1.5 Typical RAOs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.2 Nonlinear seakeeping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1.2.1 Roll motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1.2.2 Surge Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Environmental conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.1 Sea condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.2 Wind condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Data input 13

3.1 Main Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 Lines of the ship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3 Lateral areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.4 Lightship distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.5 Loading condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.6 Free surface correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.7 Intact stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.8 Cross-curves of stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.9 Bilge keel dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.10 Bridge height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.11 Size range of the examined vessels . . . . . . . . . . . . . . . . . . . . . . . . . . 183.12 Sea conditions to be examined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4 Examination 19

4.1 Vessel No. 01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

I

Contents

4.2 Vessel No. 02 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.3 Vessel No. 03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.4 Vessel No. 04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.5 Vessel No. 05 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.6 Vessel No. 06 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.7 Vessel No. 07 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.8 Vessel No. 08 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.9 Vessel No. 09 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.10 Vessel No. 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.11 Vessel No. 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.12 Vessel No. 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.13 Vessel No. 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.14 Vessel No. 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.15 Vessel No. 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5 Evaluation 43

5.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.2 Consequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.3 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.3.1 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.3.2 Roll damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.3.3 Lines of the ship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.3.4 Other . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6 Detailed examination 47

6.1 Variation of the GM values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6.1.1 Small vessel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6.1.2 Midsized vessel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.1.3 Large vessel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6.1.4 Comparison of the simulation results . . . . . . . . . . . . . . . . . . . . . 50

6.2 Rolling behavior of the large vessels . . . . . . . . . . . . . . . . . . . . . . . . . . 51

6.2.1 Large Vessel No. 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

6.2.2 Large Vessel No. 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

7 Conclusions 57

A Vessel data 59

A.1 Vessel No. 01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

A.2 Vessel No. 02 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

A.3 Vessel No. 03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

A.4 Vessel No. 04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

A.5 Vessel No. 05 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

A.6 Vessel No. 06 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

A.7 Vessel No. 07 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

A.8 Vessel No. 08 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

A.9 Vessel No. 09 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

A.10 Vessel No. 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

A.11 Vessel No. 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

A.12 Vessel No. 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

A.13 Vessel No. 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

II

Contents

A.14 Vessel No. 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72A.15 Vessel No. 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

B Variation of the bilge keel area 75

C Variation of the ship's speed 77

Bibliography 79

III

Contents

IV

List of Figures

2.1 Calculation model for the RAO determination . . . . . . . . . . . . . . . . . . . . 6

2.2 Typical RAOs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Jonswap spectrum for H1/3 = 7, 5m and Tp = 11 s . . . . . . . . . . . . . . . . . 11

3.1 Lines plan of one of the examined vessels . . . . . . . . . . . . . . . . . . . . . . . 13

3.2 Lightship distribution of one of the examined vessels . . . . . . . . . . . . . . . . 14

3.3 Bilge keel area distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.4 Bridge height above ballast arrival waterline . . . . . . . . . . . . . . . . . . . . . 17

3.5 Vessels size range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.1 Lines plan and lateral areas of Vessel No. 01 . . . . . . . . . . . . . . . . . . . . 19

4.2 Transversal acceleration on the bridge of Vessel No. 01 in accident situation 3 . 20





























5.1 Transversal accelerations on the bridge against GMsolid . . . . . . . . . . . . . . . 44

V

List of Figures

6.1 Vessel No. 13 in ballast arrival �oating condition: Variation of GMsolid . . . . 486.2 Vessel No. 01 in ballast arrival �oating condition: Variation of GMsolid . . . . 496.3 Chicago Express in ballast arrival �oating condition: Variation of GMsolid . . 506.4 Comparison of the stability in�uence for the three vessels in accident situation 1 516.5 Vessel No. 15: Variation of GMsolid in CE alike loading condition . . . . . . . 536.6 Vessel No. 11: Variation of GMsolid in di�erent loading conditions . . . . . . . 55

B.1 Vessel No. 13 in ballast arrival loading condition; Variation of the bilge keelarea; Accident situation 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

C.1 Vessel No. 13 in ballast arrival loading condition; Variation of ship's speed; Seaconditions of accident situation 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

VI

List of Tables

3.1 Accident situations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.1 Main dimensions of Vessel No. 01 . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.2 Results of the seakeeping calculation for Vessel No. 01 . . . . . . . . . . . . . . 20





























6.1 Stability data for the small vessel . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.2 Stability data for the midsized vessel . . . . . . . . . . . . . . . . . . . . . . . . . 49

6.3 Stability data for the large vessel . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

6.4 Loading condition of the Chicago Express during its accident . . . . . . . . . 52

6.5 Vessel No. 15: CE alike �oating condition . . . . . . . . . . . . . . . . . . . . . 52

6.6 Vessel No. 15: Transversal accelerations for CE alike loading conditions . . . . 53

6.7 Vessel No. 11: Chicago Express alike �oating condition . . . . . . . . . . . . 54

6.8 Vessel No. 11: Transversal accelerations for CE alike loading conditions . . . . 54

6.9 Vessel No. 11: New �oating condition . . . . . . . . . . . . . . . . . . . . . . . 54

VII

List of Tables

6.10 Vessel No. 11: Transversal accelerations for new loading conditions . . . . . . . 55

A.1 Detailed main dimensions, Vessel No. 01 . . . . . . . . . . . . . . . . . . . . . . 59A.2 Detailed main dimensions, Vessel No. 02 . . . . . . . . . . . . . . . . . . . . . . 60A.3 Detailed main dimensions, Vessel No. 03 . . . . . . . . . . . . . . . . . . . . . . 61A.4 Detailed main dimensions, Vessel No. 04 . . . . . . . . . . . . . . . . . . . . . . 62A.5 Detailed main dimensions, Vessel No. 05 . . . . . . . . . . . . . . . . . . . . . . 63A.6 Detailed main dimensions, Vessel No. 06 . . . . . . . . . . . . . . . . . . . . . . 64A.7 Detailed main dimensions, Vessel No. 07 . . . . . . . . . . . . . . . . . . . . . . 65A.8 Detailed main dimensions, Vessel No. 08 . . . . . . . . . . . . . . . . . . . . . . 66A.9 Detailed main dimensions, Vessel No. 09 . . . . . . . . . . . . . . . . . . . . . . 67A.10 Detailed main dimensions, Vessel No. 10 . . . . . . . . . . . . . . . . . . . . . . 68A.11 Detailed main dimensions, Vessel No. 11 . . . . . . . . . . . . . . . . . . . . . . 69A.12 Detailed main dimensions, Vessel No. 12 . . . . . . . . . . . . . . . . . . . . . . 70A.13 Detailed main dimensions, Vessel No. 13 . . . . . . . . . . . . . . . . . . . . . . 71A.14 Detailed main dimensions, Vessel No. 14 . . . . . . . . . . . . . . . . . . . . . . 72A.15 Detailed main dimensions, Vessel No. 15 . . . . . . . . . . . . . . . . . . . . . . 73

VIII

Nomenclature

Symbol Unit Meaning

ABK

[m2]

Total bilge keel areaatmax [m/s2] Maximum occurring transversal accelerationB [m] Ship's breadthcB [−] Block coe�cientD [m] Depth to freeboard deck4 [t] Displacement of the shipg [m/s2] Gravitational acceleration which is 9.81m/s2

GMcorrected [m] Metacentric height with free surface correctionGMsolid [m] Metacentric height without free surface correctionGZ [m] Righting leverH1/3 [m] Signi�cant wave height

KG [m] Vertical center of gravityLOA [m] Length over allLPP [m] Length between the perpendicularsϕmax [◦] Maximum occurring rolling angleTD [m] Design draftTP [s] Peak wave periodTS [s] Signi�cant wave periodv [kts] Ship's speed

Abbreviation Meaning

a. B.L. above baselineAP After PerpendicularBSU Bundesstelle für Seeunfalluntersuchung; Federal Bureau of Maritime

Casualty InvestigationDNV Det Norske VeritasE4 A method database for ship designFP Forward PerpendicularHSVA Hamburgische Schi�bau- Versuchs AnstaltIMO International Maritime OrganisationPRADS International symposium on PRActical Design and other �oating

StructuresRAO Response Amplitude OperatorTEU Twenty feet Equivalent UnitTUHH Technische Universität Hamburg-Harburg; Hamburg University of

Technology

IX

List of Tables

X

1 Introduction

In the years 2008/2009 the world economic crisis caused a reduction in the number of transportedTEU, due to a signi�cant decrease in transported goods. Consequently a great number of con-tainer vessels had been laid up or were forced to operate with a small amount of cargo on board.In this loading condition container vessels have a very high stability. In many cases their verticalcenter of gravity is even located below the lightship condition's coordinate. This is due to largeamounts of ballast water in wing and double bottom tanks as well as no or only a small amountof cargo located at cargo hold bottom. The high amount of ballast water is needed to obtain anadequate hull and propeller immersion as well as a limitation of the longitudinal bending mo-ments within the hull structure. In the typical loading conditions with higher amounts of cargo,less ballast water is needed and the stability is lower. Under the described circumstances, severalaccidents have happened to container vessels during the last years. The accidents caused not onlysevere damages on ships but also heavily injured and even killed crew members. They have beenthrown through the bridge due to high transversal accelerations caused by heavy roll motionsof the ship. This highlights, that modern container ship designs face some problems concerninginsu�cient seakeeping behavior. Since several accidents have happened to ships sailing underGerman �ag, the BSU analyzed them by default. For three of the accidents, the seakeepingbehavior has been examined in detail by order of the BSU at the institute of ship designand ship safety at the Hamburg University of Technology (TUHH) [1][2][3]. Thisthesis shall examine the seakeeping behavior of several typical container vessels in equivalentenvironmental conditions.

1.1 Key data of the three examined accidents

The examinations revealed signi�cant parallels between the accidents. They all happened undercomparable environmental and loading conditions.

� All ships followed the standard procedure for heavy weather. This means, that they headinto the sea at slow speeds to minimize the risk of damaging the ship's bow structure dueto high slamming forces and green water on deck.

� All ships encountered large rolling angles of more than 30◦.

� Due to the excessive stability and the therefore short roll periods of the ships, the high rollangles resulted in transversal accelerations of up to 14m/s2.

In the following, an overview of the environmental conditions and several ship data for thethree examined accidents is given. More detailed information about the accidents and theircircumstances may be extracted from the respective investigation reports.

1.1.1 Accident of the CMS Chicago Express [1]

� The accident happened on September 24th, 2008 during heavy weather in the SouthChina Sea near Hong Kong.

1

1 Introduction

� During the accident the waves had a signi�cant period of approximately TS = 9 ... 10 s anda signi�cant wave height of H1/3 = 7.5m.

� The encountering angle between the vessel and the waves was about 120◦... 150◦ (with 0◦

from astern).

� The ship operated at low speeds of about v = 2 ... 4 kn.

� The ship was lightly loaded, which resulted in KG = 15.647m (free surface correctionincluded) and GMcorrected = 7.712m.

� The maximum rolling angle was about 35◦.

� The maximum transversal accelerations on the bridge exceeded 1.0 g.

� One crew member was killed, one heavily injured and several slightly injured.

� No noticeable damages to the vessel's hull.

1.1.2 Accident of a 2468 TEU container vessel [2]

� The accident happened on September 15th, 2009 during heavy weather in the SouthChina Sea near Hong Kong.

� During the accident the waves had a signi�cant wave period of TS = 8 ... 9 s and a signi�cantwave height of about H1/3 = 7m.

� The encountering angle between the vessel and the waves was about 120◦... 150◦.

� The ship operated at low speeds of about v = 2 ... 3 kn.

� The ship was lightly loaded which resulted in KG = 9.696m (free surface correctionincluded) and GMcorrected = 5.627m.

� The documented longitudinal bending moment was higher than the admissible value.



� One crew member was killed.

� Heavy damages to the vessel's hull occurred.

1.1.3 Accident of a 2500 TEU container vessel [3]

� The accident happened on October 16th, 2009 during heavy weather in the North Seanear Borkum.

� During accident the waves had a signi�cant wave period of TS = 9 ... 10 s and a signi�cantwave height of about H1/3 = 7m.

� The encountering angle between the vessel and the waves was about 120◦... 130◦.

� The ship operated at low speeds of about v = 5 kn.

� The ship was lightly loaded which resulted in KG = 10.45m (free surface correctionincluded) and GMcorrected = 4.56m.

2

1.2 Following objectives for the diploma thesis



� One crew member was heavily injured.

� No damages to the vessel's hull occurred.

1.2 Following objectives for the diploma thesis

Due to the many similarities between the above mentioned three accidents, the question arises,whether other conventional container vessels also would encounter such high rolling angles andaccelerations on the bridge under the accident conditions named above.According to the actual intact stability code IMO A.749(18)[4], an approved trim and stability

booklet for each ship has to contain some standard loading conditions. Of those, the ballastarrival loading condition matches the loading condition of the ships in accident best. In thisloading condition the ship operates without cargo, with 10% bunker and stores as well as enoughballast water for su�cient immersion of the hull. The propeller has to be immersed for adequatepropulsion. Additionally the fore ship has to be immersed su�ciently to reduce slamming forceson the forward bottom shell. This results in a small KG and respectively a high GM.Furthermore �lled ballast water tanks in the fore or aft part of the ship cause high, longitudinal

bending moments to the ship's hull. The ship has to be ballasted, so the maximum allowedbending moment is not exceeded.Container ships in the ballast arrival loading condition operate always with a relatively high

negative trim. Negative means, the ship's draught at the aft perpendicular is higher. The ballastarrival loading condition is mandatorily indicated to be a seagoing condition.

Therefore the scope of this thesis is to examine, if container vessels in ballast

arrival loading condition have an increased risk of accident in heavy seas due to the

design of this speci�c ship type.

For this reason a larger number of container vessels of various size is analysed in the ballastarrival loading condition . The goal is to determine the seakeeping behavior for each vessel whenit is encountering the three aforementioned accident situations. So the maximum rolling angleand the maximum transversal acceleration on the bridge are calculated, to estimate the riskof accident. All needed calculations are performed with the ship design software E4, which isavailable at Hamburg University of Technology (TUHH). A detailed description of theutilised methods can be found in chapter 2. In addition approaches to reduce the risk of accidentshall be provided, examined and evaluated.

3

1 Introduction

4

2 Theory

2.1 Description of the utilised seakeeping simulation method

For the determination of the seakeeping behavior, E4 includes a simulation method developedby Söding in connection with the investigation of the capsizing accident of the E.L.M.A Tresin 1987 [5]. The method has been further developed by Kröger [6] and in the scope of severalresearch projects at the TUHH which led to the actual seakeeping method E4ROLLS. Thefollowing explanations are based on Krüger [7], Kluwe [8] and the investigation reports ofthe three accidents [1][2][3] described in chapter 1.1.The method is capable of simulating the motion of a ship within the time domain. At this all

six degrees of freedom of a ship are described. Further it is possible to enter regular or irregular,as well as short or long crested seaways. The method is explained brie�y in the following chapter.

2.1.1 Linear strip method

In the E4 seakeeping method a linear RAO is determined for each of the six degrees of freedom.The RAOs are calculated by means of a strip method in the frequency domain. Each set of sixRAOs applies for one vessel's speed. Therefore one set of RAOs has to be calculated for eachspeed examined.Four of the degrees of freedom, namely sway, heave, pitch and yaw are calculated linearly using

the respective RAOs. A link to the nonlinear motions is considered. It is assumed, that theamplitudes of these four motions stay moderate and that the hydrodynamic in�uences outweighthe nonlinearities. Therefore it is adequate to incorporate them linearly. Due to the linearisationof the sway and yaw motion, the method is not able to describe broaching in following sea, whichoften causes high roll motions and implicates an enhanced danger of capsizing. For the samereason the method overestimates the ship's motions in beam seas at low speeds. This is relatedto an underestimation of the drift motion in beam direction.

2.1.1.1 Calculation model

The lightship weight and the deadweight distribution are represented by a cuboid for each anal-ysed vessel. The cuboid and the ship have equivalent mass moments of inertia. Its height andwidth shown in �gure 2.1 are governed by the extension of the light-ship and the loading weight.The cuboid and the hull form are then used to calculate the RAOs.

5

2 Theory

Figure 2.1: Calculation model for the RAO determination

2.1.1.2 Roll radius of inertia and roll period

Before calculating the respective RAO sets, the roll radius of inertia of the ship as well as theroll period are calculated. The roll period applies for still water condition and small rollingangles. For the roll radius of inertia two values are calculated based on the ship's weight withand without the in�uence of section added masses, which consider the in�uence of the water,surrounding the ship's hull. Normally the roll radius of inertia with the in�uence of section addedmasses shall not exceed values of about 0.45B for container vessels.

For the examined vessels in ballast arrival loading condition, the dry roll radius of inertiareaches a value between 0.33B ... 0.37B . The wet roll radius of inertia reaches values between0.40B ... 0.42B. So the used models are reasonable. The estimated roll periods reach valuesbetween 9.5 s ... 11 s.

2.1.1.3 Roll damping

It can be stated that the damping of a ship's roll motion is relatively small compared to e.g.the damping of the heave or pitch motion. Therefore large roll angles may occur in a resonancecondition. This indicates that the assumption of a correct roll damping is mandatory. Thedirect, theoretical calculation of the roll damping is not possible until now. Only the dampingdue to wave radiation can be calculated with potential theory methods. But there are manyother highly nonlinear and also viscous e�ects to consider.

6


For this reason Blume [9] developed roll damping coe�cients, based on practical experimentsof ships in model scale. With these empirical coe�cients the roll damping can be corrected to amore realistic value. At this the correction includes also the damping in�uence of the bilge keels.The roll damping in E4ROLLS is considered with these coe�cients of similar ships.

2.1.1.4 Calculation settings

The calculations for higher speeds (v > 18 kn) and short wave lengths lead to problems for thesurge, sway and yaw motion RAOs, which are reaching disproportionately high values or becomesingular. Consequently the problematic short wave lengths are excluded for higher speeds.

7

2 Theory

2.1.1.5 Typical RAOs

Typical RAOs for the six degrees of freedom are shown in �gure 2.2 for one of the examinedvessels. In the graphs the RAOs are plotted against the wavelength. Each curve represents oneencounter angle of the ship into the seaway. A number of seven encounter angles between 0◦

(waves from astern) and 180◦ (waves from ahead) is indicated in each graph.

Figure 2.2: Typical RAOs

2.1.2 Nonlinear seakeeping

The remaining two degrees of freedom, namely surge and roll are treated di�erently. For instancethe link to the linear motions or the exciting hydrodynamic forces and moments for the rollmotion are considered linearly using a RAO. But due to factors such as the high amplitude of

8


the roll motion or the highly nonlinear restoring moments, the surge and roll motion have tobe simulated nonlinearly in the time domain. The linearisation of the roll motion for example,would imply replacing the lever arm curve with a straight line having a gradient correspondingto GM. It is easy to understand, that such a simpli�cation is not permissible. Therefore theroll and the surge motion are simulated nonlinearly in the time domain, based on the formulasdescribed in the following.

2.1.2.1 Roll motion

The roll motion is calculated in the time domain according to the equation of motion 2.1 shownbelow:

ϕ̈ =Ixz

[(ψ̈ + ψϕ̇2

)cosϕ−

(ϑ̈+ ϑϕ̇2

)sinϕ

]−m

(g − ζ̈

)hs

Ixx − Ixz (ψ sinϕ+ ϑ cosϕ)(2.1)

+MWind +MSway&Y aw +MWave +MTank −MD

Ixx − Ixz (ψ sinϕ+ ϑ cosϕ)

with

� ϕ, ϑ and ψ, the angles to describe roll, pitch and yaw as well as ζ describing the heave

direction which coincides with z of the hull-bound coordinate system.

� hs, the righting lever in seaway according to Grim's [10] equivalent wave method.

� m is the mass of the ship and g is the gravitational acceleration.

� MWind, MSway&Y aw, MWave and MTank , the exiting roll moments due to wind, sway andyaw, waves and �uid in tanks or �ooded compartments.

� MD, the nonlinear damping moment depends on ship's speed. It is determined by usingdamping coe�cients according to Blume [9].

� Ixx and Ixz are the moment of inertia and the centrifugal moment.

Before the simulation is started, the cross curves of the ship are calculated, to avoid the time-consuming calculation of the actual righting lever in seaways for each time step of the simulation.The actual value during simulation is interpolated from the pre-calculated righting levers usingGrim's [10] equivalent wave method.

2.1.2.2 Surge Motion

Finally, the surge motion is simulated based on the ship's resistance, speed, mass (including addedhydrodynamic mass) and surge-inducing wave forces. The wave force is calculated, assuming ahydrostatic pressure distribution under the water surface at half of ship's draught. This means,that at each frame the force of buoyancy is perpendicular to this line of equivalent pressure athalf draught. The surge motion is simulated based on the approach 2.2 below.

ξ̈ = −[2R (v0)

v0m∗ ξ̇ +R (vo)

v20m∗ ξ̇

2 +4Rm∗

](2.2)

with

� R, representing the resistance curve in still water conditions

9

2 Theory

� 4R, the added resistance due to waves

� v0, the ship's mean speed

� m∗, the ship's mass with a part of hydrodynamic mass

2.1.3 Conclusion

The described method has been evaluated and approved in the scope of various research projectsat the TUHH including extensive model test at the HSVA. In addition the accident examinationreports [1][2][3] prove, that it was possible to anticipate exactly the seakeeping behavior of thevessels in the respective accident situations.

Due to the application of Grim's [10] equivalent wave, the method computes reasonablyfast. Therefore it is possible to obtain realistic results for the seakeeping behavior of ships invarious seaways within short calculation time. For the same reasons, the method has the namedlimitations of simulating the seakeeping behavior in beam seas and of describing the broachingin following seas. Considering these limitations, it is a very suitable method to calculate headand following seas.

2.2 Environmental conditions

The seakeeping method of E4 is able to simulate various types of seaways with or without wind.

2.2.1 Sea condition

The most elementary seaway, which may be generated, is a seaway of regular waves. The wavesin this seaway have just one direction and a constant wave period. Such seaways do not existin nature and can only be generated in a model tank. Natural seaways are usually representedby superposed regular waves of di�erent frequencies and encounter directions. A frequencydistribution appearing in nature is respected by applying a wind sea spectrum like the Pierson-Moskowitz 1 or the Jonswap2 spectrum. These spectra are based on extensive measurementsof real seaways. The encounter directions are calculated randomly according to a manually chosennumber of directions. This leads to a more realistic, random seaway with either short-crested orlong-crested waves, depending on a small or large number of encounter directions.

Another problem may be, that real seaways mostly consist of a wind sea part, generated by theactual wind and a swell part, remaining from former wind conditions. Hence for examinationsin seaways containing a high swell part, it may be reasonable to generate a seaway based on aso called multi-peak spectrum. Such a spectrum has two peaks in the frequency distribution.One wide-band peak for the wind sea part and one narrow-band peak for the swell part of theseaway.

But the following calculations are based on heavy seaways, where the wind sea part is essential.Therefore it is decided to use a Jonswap-spectrum in combination with short-crested waves.With a given signi�cant wave height H1/3 and a signi�cant wave period Ts a seaway is generated,which is considered being matching best a natural wind sea seaway. The wave height H1/3 isthe average wave height (trough to crest) of the one-third largest waves, while the signi�cantwave period Ts is the associated average wave period of the one-third largest waves. A typicalJonswap spectrum for a constant signi�cant wave height of H1/3 = 7.5m and a constant peak

1A spectral form for fully developed wind seas proposed by Pierson and Moskowitz (1964)2A corrected Pierson Moskowitz spectrum with data from the JOint North SeaWAve Project by Hasselmannet al. (1973)

10

2.2 Environmental conditions

period of Tp = 11 s is shown in �gure 2.3, where the energy density spectrum S (ω) is shownagainst the wave circular frequency ω.

Figure 2.3: Jonswap spectrum for H1/3 = 7, 5m and Tp = 11 s

2.2.2 Wind condition

It is possible to consider the in�uence of incoming wind on the seakeeping behavior. The govern-ing factor for the wind induced rolling moments is the size of the lateral areas facing the wind.The lateral area of a container vessel in the ballast arrival loading condition is relatively small,because no containers are stowed on deck. The wave induced rolling moments are signi�cantcompared to the wind induced moments and the wind in�uence can be neglected. Therefore itis decided to determine the seakeeping behavior without wind in the scope of the thesis.

11

2 Theory

12

3 Data input

The thesis is written based on vessel data which are available at the institute of ship designand ship safety. Overall 15 container vessels are examined in this thesis.

Before the calculations and simulations are started, extensive numerical models are generated.For each vessel a general arrangement plan, a tank capacity plan and a stability booklet areavailable. The lines of the ships for all vessels are also available. With these documents enoughtechnical data are available for the calculation of the seakeeping behavior. In detail, the followingdata are entered and/or veri�ed in the E4 software for each vessel which is examined.

3.1 Main Dimensions

All available main dimensions are entered into the system. These are geometrical dimensionslike the length between perpendiculars LPP , the length over all LOA, the breadth B, the depthto freeboard deck D or the design draft TD. Further entered dimensions worth mentioning, arethe keel thickness and the shell plating factor, which are needed to calculate the cross-curves ofstability as described in chapter 3.8.

3.2 Lines of the ship

For the intended calculations, the utilized model needs to match the original with adequate ac-curacy. Therefore the available lines of the ship in E4 are checked and corrected where necessary.A typical lines plan of one of the examined vessel is shown in �gure 3.1.

Figure 3.1: Lines plan of one of the examined vessels

3.3 Lateral areas

The front and side lateral areas also shown in �gure 3.1 are entered to be able to include winde�ects in the seakeeping calculations. In addition the side lateral area is very useful to assess thedimensions of the cuboid for the RAO calculations, as it is explained in chapter 2.1.1.1. Lateron it is decided, not to consider the in�uence of the wind on the seakeeping behavior in the �rststep.

13

3 Data input

3.4 Lightship distribution

The cuboid for determining the RAOs is calculated, based on the respective vessel's lightshipweight and the deadweight distribution as well as their extensions. Normally a detailed lightshipdistribution in longitudinal direction is not necessary for seakeeping calculations. A coarse light-ship weight distribution is su�cient, for the same reasons which are shown in chapter 2.1.1.1.Anyhow, with regard to potential longitudinal strength calculations in later examinations, foreach vessel a detailed lightship weight distribution is used for further analysis. Such calcula-tions are performed to ensure su�cient structural strength. The ship's structure is loaded bylongitudinal bending moments as well as shear forces due to torsion of the hull. Therefore a de-tailed weight distribution is mandatory for longitudinal strength calculations. Picture 3.2 showsa typical lightship weight distribution of one of the examined vessels.

Figure 3.2: Lightship distribution of one of the examined vessels

3.5 Loading condition

As stated at the beginning, this analysis is concentrated on the ballast arrival loading condi-tion. It is transferred to the models according to the information stated in the stability booklet.The ballast arrival displacement consists of the lightship weight and the respective deadweight,whereas the deadweight includes the weight of the ballast water, bunker and freshwater. Worthmentioning is the fact, that in the analysed loading condition no cargo is on board. For simpli-�cation, the deadweight is approximated as one weight item. Thus there is one speci�c centerof gravity and the weight item's extension over the whole ship. The reasons for this coarsepresumption are given in chapter 2.1.1.1.

14

3.6 Free surface correction

3.6 Free surface correction

When tanks are partly �lled in a loading condition, the free surface of the containing �uidin�uences the stability of the ship. The liquid's center of gravity moves when the ship heels.This leads to an apparent reduction of the GM . The corrected GM is usually determined bythe formula 3.1 shown below

GMcorrected = GMsolid −∑i

ρliquid i · Itank i

4(3.1)

for each partly �lled tank i with the particular density of the liquid in tank ρliquid, the particularmoment of inertia of the free surface Itank and the displacement 4 belonging to the particularloading condition .For the quasi-static intact stability analysis, this procedure is permissible. But for the highly

nonlinear motions of a ship in seaways the correction is inaccurate, because the damping e�ectof the sloshing �uid in the tank is not considered. For example this e�ect is used intentionallyin roll damping tanks.For the seakeeping calculations it has been �gured out, that both e�ects (roll damping due to

sloshing and stability reduction due to the free surface) approximately compensate each other.Therefore the seakeeping calculations in E4 are always performed with an uncorrected GMsolid.

3.7 Intact stability

The intact stability is calculated according to the intact stability code of the IMO [4]. It isperformed to determine the limiting intact stability criterion in the examined ballast arrivalloading condition. The following six criteria are considered:

1. The initial metacentric height GM0 (including free surfaces) shall not be less than 0.15m.(named in the following: Initial GM is 0.15m)

2. The righting lever GZ shall be at least 0.2m at an angle of heel equal to or greater than30◦. (named in the following: GZ is 0.2 at 30◦)

3. The maximum righting lever shall occur at an angle of heel not less than 25◦. (named inthe following: Max. GZ at 25◦)

4. The area under the GZ curve shall not be less than 0.055metre− radians up to 30◦ angleof heel. (named in the following: Area (0, 30) = 0.055m · rad)

5. The area under the GZ curve shall not be less than0.09metre − radians up to 40◦ angleof heel. (named in the following: Area (0, 40) = 0.090m · rad)

6. The area under the GZ curve between the angles of heel of 30◦ and 40◦ shall not be lessthan 0.03metre− radians. (named in the following: Area (30, 40) = 0.030m · rad)

3.8 Cross-curves of stability

Furthermore the cross-curves of stability of the hull for �xed and free trim are calculated. Theresulting curves in E4 are compared to the curves derived from the stability booklet. The betterthe curves match, the better the E4 calculation model matches the calculating model of theshipyard. Thereby its assured, that the result of the calculations are applicable to the realizedvessel.

15

3 Data input

At this the cross-curves for small angles should have approximately equivalent values. For largeangles (> 60◦), the values may di�er. This is due to the not considered hatchway coamings in thecalculation models. In the scope of the subsequent analysis, this simpli�ed model is consideredto be applicable, because the vessels never reach higher rolling angles than ∼ 40◦.

3.9 Bilge keel dimensions

During seakeeping calculation, the bilge keel dimensions have to be considered. They are neededto determine their e�ect on the ship's roll damping. Because the bilge keel area is not given forsome ships, the value then has to be estimated. Therefore a mean value is calculated out of thegiven bilge keel dimensions with equation 3.2 as follows:

mean value =1

n

n∑i=1

Lpp i

ABK i

∼= 5.36 [1/m] (3.2)

with the index for each ship i, the total number of ships with given bilge keel dimensions n, thebilge keel area ABK and the length between perpendicular Lpp of the respective ship. Accordingto the mean value, the bilge keel area for ships without given value is estimated by:

ABK i =Lpp i

5.36

[m2]

(3.3)

Figure 3.3 shows the distribution of the respective bilge keel area against Lpp. The numbersabove the entries indicate the number of the examined vessel according to chapter 4.

15

14

13

12

11

10

9

8

75

4

3

21

6

30,00

40,00

50,00

60,00

70,00

80,00

90,00

100,00

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330

LPP [m]

Bil

ge k

eel

are

a [

m2]

Actual values of examined vessels Mean value curve

estimated values

Figure 3.3: Bilge keel area distribution

16

3.10 Bridge height

3.10 Bridge height

The severely and fatally injured crew members mentioned in the beginning, have been on dutyon the vessel's bridge when the accident occurred. Hence the transversal accelerations a�ectinga human on the bridge are calculated in the further scope of this thesis. The transversal acceler-ations in seaways are calculated at one meter above the bridge deck. This value is assumed forthe vertical center of gravity of a human.For the roll behavior of a ship in seaway it can be estimated, that its roll axis is located in

the proximity of the vessel's line of �oatation according to Abdel-Maksoud [11]. This is whythe transversal accelerations are inherently higher on the bridge than on lower decks. In thisexamination, the line of �oatation is the ballast arrival loading condition waterline. The bridgeheight above the ballast arrival waterline of the 15 vessels against LPP is shown in �gure 3.4.

Actual values of examined vessels

15

14

13

12

11

9

8

7

6

5

4

3

2

1

30,0

31,0

32,0

33,0

34,0

35,0

36,0

37,0

38,0

39,0

40,0

41,0

42,0

200 210 220 230 240 250 260 270 280 290 300 310 320 330

Lpp [m]

Heig

ht

of

bri

dg

e a

bo

ve b

all

ast

arr

ival

wate

rlin

e [

m]

Actual values of examined vessels

Figure 3.4: Bridge height above ballast arrival waterline

17

3 Data input

3.11 Size range of the examined vessels

The smallest examined vessel is nearly 200m whereas the largest vessel is more than 320mlong. Figure 3.5 opposes the displacement to the length between perpendicular. To visualise thedi�erences between the examined vessels, the lateral view of three of them is given. The detailedship data and main dimensions for each ship are given in the respective section of chapter 4.

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

30000

40000

50000

60000

70000

80000

90000

100000

110000

120000

130000

190 200 210 220 230 240 250 260 270 280 290 300 310 320 330

LPP [m]

Dis

pla

cem

en

t at

Td

es

ign [

t]

Figure 3.5: Vessels size range

3.12 Sea conditions to be examined

According to the accident sea conditions named in chapter 1.1, the following situations are exam-ined. As mentioned in chapter 2.2, the seaway is described by a signi�cant wave period TS anda signi�cant wave height H1/3. For each analysed vessel a speed v and a wave encountering angleis assumed according to the respective accident situation. The encountering angle is measuredfrom astern, so 0◦ means the ship encounters a following sea.

Table 3.1: Accident situations

Accident

situation

Corresponds to theaccident of

v [kts]Encount.angle [◦]

TS [s] H1/3 [m]

Situation 1 Chicago Express 3 150 9.5 7.5

Situation 2 2468 TEU vessel 3 150 8.5 7.0

Situation 3 2500 TEU vessel 5 130 9.5 7.0

18

4 Examination

For each vessel the seakeeping behavior during the three accident situations is determined. Thissimulation extends to 20, 000 time steps, having a step size of 0.5 s each. This corresponds to atotal duration of the simulation in real time of 10, 000 s.This chapter explains the data sets for all analysed vessels. The compilation contains a sim-

pli�ed lines plan including the lateral areas and a few main dimensions. A detailed list of allmain dimensions and the data for the respective ballast arrival loading condition can be foundin the appendix A. In addition, some speci�c characteristics of the ship are named. (e.g. thequality of the calculation model or the hullform). At this the explanations concerning the abilityof passing the Panama Canal, apply on the canal before its enlarging, which will be completedin the year 2014/2015. Further with the referenced cB value for each vessel, the �neness of thehull forms is described and can be compared to other vessels.Furthermore the maximum rolling angles and maximum transversal accelerations on the bridge

are given, resulting from each of the three above named accident situations. For the worst sce-nario the statistical distribution of the occurring accelerations is given by a histogram, where themaximum transversal acceleration is derived from. The mean value of the normalized amplitudesand the associated standard deviation as well as the number of calculated periods in the simu-lation time of 10, 000 s are also shown in the histogram. It is to be noted, that the histogramsdo not have the same scale on their x-axis. So the histograms of two di�erent vessels can not becompared directly. The order of the analysed vessels is randomly chosen.

4.1 Vessel No. 01

Figure 4.1: Lines plan and lateral areas of Vessel No. 01

Table 4.1: Main dimensions of Vessel No. 01

Main dimensions Value Unit

Lpp 263.00 [m]

B 40.00 [m]

TD 12.00 [m]

Containers 5,512 [TEU]

The �rst analysed vessel has the geometric capacity to carry 5, 512TEU . Having the maindimensions according to table 4.1, this vessels must be classi�ed as a smaller Post-Panamax

19

4 Examination

vessels. The following characteristics of Vessel No. 01 are to be noted:

� The lines of the ship shown in �gure 4.1 have a cB value of 0.57 on design draft.

� The documented bilge keel area is smaller than the mean value according to chapter 3.9.

� The stability in the ballast arrival loading condition is very high resulting inGMsolid = 10.43m.

� The limiting intact stability criterion (Max. GZ at 25◦) requires a GMmin = 1.89m.

The calculated transversal accelerations on the bridge and the rolling angles for the three accidentconditions are listed in table 4.2.

Table 4.2: Results of the seakeeping calculation for Vessel No. 01

Accidentsituation

atmax

[m/s2

]ϕmax [◦]

Situation 1 12.5 32

Situation 2 12.5 29

Situation 3 13.5 34

The maximum acceleration occurs for accident situation 3. With atmax = 13.5m/s2 for accidentsituation 3 the examination already starts with a signi�cant value. The statistical distributionof the transversal accelerations in this situation is shown in �gure 4.2.

Figure 4.2: Transversal acceleration on the bridge of Vessel No. 01 in accident situation 3

20

4.2 Vessel No. 02

4.2 Vessel No. 02




Lpp 292.00 [m]

B 40.00 [m]

TD 12.00 [m]


The second analysed vessel has the geometric capacity to carry 6, 500TEU . Having the maindimensions according to table 4.3, it belongs to the medium sized Post-Panamax vessels. Thefollowing characteristics of Vessel No. 02 are to be noted:

� The lines of the ship shown in �gure 4.3 have a cB value of 0.61 on design draft

� The documented bilge keel area is signi�cantly smaller than the mean value according tochapter 3.9.

� The stability in the ballast arrival loading condition is very high resulting inGMsolid = 9.88m.




Accidentsituation

atmax

[m/s2

]ϕmax [◦]

Situation 1 7.5 18

Situation 2 7.0 15

Situation 3 11.5 28

The maximum acceleration occurs for accident situation 3. The accelerations for VesselNo. 02 in situation 1 and 2 are signi�cant smaller than for Vessel No. 01. The statisticaldistribution of the transversal accelerations in this situation is shown in �gure 4.4.

21

4 Examination


4.3 Vessel No. 03




Lpp 263.00 [m]

B 40.00 [m]

TD 12.50 [m]


The third analysed vessel has the geometric capacity to carry 5, 726TEU . Having the maindimensions according to table 4.5, it belongs to the smaller Post-Panamax vessels. It has exactlythe same main dimensions and an equivalent ballast arrival loading condition as Vessel No. 01.In contrast Vessel No. 03 has a higher cB value and therefore is able to carry more TEU at aslower design speed than Vessel No. 01. The following characteristics of Vessel No. 03 are tobe noted:

� The lines of the ship shown in �gure 4.5 have a cB value of 0.58 in design draft.

22

4.3 Vessel No. 03

� The documented bilge keel area is signi�cantly higher than the mean value according tochapter 3.9.

� The stability in ballast arrival loading condition is very high resulting in aGMsolid = 10.12m.




Accidentsituation

atmax

[m/s2

]ϕmax [◦]

Situation 1 10.5 26

Situation 2 11.0 23

Situation 3 11.0 30

The maximum acceleration occurs for accident situation 3, but the accelerations are compa-rable for each accident situation.Even though Vessel No. 01 and Vessel No. 03 are very similar, the values are smaller for

the Vessel No. 03. A possible reason for this di�erence is the 60% larger bilge keel area ofVessel No. 03 and therefore a higher roll damping, respectively. The accelerations in accidentsituation 2 and 3 are the same. Therefore the situation of both with the higher rolling angle isstated to be the worst situation. The statistical distribution of the transversal accelerations inthis situation is shown in �gure 4.6.


23

4 Examination

4.4 Vessel No. 04




Lpp 280.75 [m]

B 32.26 [m]

TD 11.00 [m]


Vessel No. 04 has the geometric capacity to carry 4, 402TEU . Having the main dimensionsaccording to table 4.7, it complies with the maximum possible main dimensions to pass throughthe Panama Canal. The vessel is the �rst typical Panamax container vessel, analysed withinthis examination. The following characteristics of Vessel No. 04 are to be noted:


� The bilge keel area is not documented for this vessel and is estimated according to chapter3.9.

� The stability in ballast arrival loading condition is less high resulting in a GMsolid = 6.39m.

� The limiting intact stability criterion (Area (30, 40) = 0.030m · rad) requires aGMmin = 0.16m.

In general typical Panamax vessels with its large L/B ratio tend to small intact stability values.For Vessel No. 04 this leads to a very small GMmin in ballast arrival loading condition. The cBvalue of 0.69 is the highest value of the analysed vessels. The calculated transversal accelerationson the bridge and the rolling angles for the three accident conditions are listed in table 4.8.


Accidentsituation

atmax

[m/s2

]ϕmax [◦]

Situation 1 9.0 21

Situation 2 8.0 18

Situation 3 12.0 31

The maximum acceleration occurs for accident situation 3. As already for Vessel No. 02, theoccurring transversal accelerations for accident situation 1 and 2 are signi�cant smaller than for

24

4.5 Vessel No. 05

accident situation 3. The statistical distribution of the transversal accelerations in this situationis shown in �gure 4.8.


4.5 Vessel No. 05




Lpp 221.00 [m]

B 32.20 [m]

TD 11.82 [m]


The 5th examined vessel has the geometric capacity to carry 3, 323TEU . Having the maindimensions according to table 4.9, it is also able to pass the Panama Canal, but it is shorterthan Vessel No. 04. The following characteristics of Vessel No. 05 are to be noted:


25

4 Examination

� The documented bilge keel area matches the mean value according to chapter 3.9.

� The stability in ballast arrival loading condition is moderately high resulting in aGMsolid = 7.09m.




Accidentsituation

atmax

[m/s2

]ϕmax [◦]

Situation 1 12.0 32

Situation 2 13.0 36

Situation 3 13.0 35

For the seaways of accident situation 2 and 3, the same maximum transversal accelerations onthe bridge occur while the accelerations in accident situation 1 are also nearly as high. Becausethe rolling angle of situation 2 is the highest, this situation is stated to be the most critical. Thestatistical distribution of the transversal accelerations in this situation is shown in �gure 4.10.


26

4.6 Vessel No. 06

4.6 Vessel No. 06




Lpp 244.51 [m]

B 32.25 [m]

TD 10.00 [m]


Vessel No. 06 has the geometric capacity to carry 4, 253TEU . Having the main dimensionsaccording to table 4.11, it is another midsized container vessel which may travel through thePanama Canal. The following characteristics of Vessel No. 06 are to be noted:







Accidentsituation

atmax

[m/s2

]ϕmax [◦]

Situation 1 9.0 23

Situation 2 11.0 25

Situation 3 12.0 29

The maximum acceleration occurs for accident situation 3. The statistical distribution of thetransversal accelerations in this situation is shown in �gure 4.12.

27

4 Examination


4.7 Vessel No. 07




Lpp 256.20 [m]

B 32.20 [m]

TD 10.00 [m]


Vessel No. 07 has the geometric capacity to carry 4, 252TEU . Having the main dimensionsaccording to table 4.13, the vessel is also a midsized, Panama canal capable container shipvery similar to Vessel No. 06. The following characteristics of Vessel No. 07 are to be noted:


� The documented bilge keel area is slightly smaller than the mean value according to chapter3.9.

28

4.7 Vessel No. 07



Compared to Vessel No. 06, the cB value of Vessel No. 07 is slightly larger and the GMmin

is slightly smaller. The calculated transversal accelerations on the bridge and the rolling anglesfor the three accident conditions are listed in table 4.14.


Accidentsituation

atmax

[m/s2

]ϕmax [◦]

Situation 1 10.0 29

Situation 2 10.0 24

Situation 3 12.0 33

As for Vessel No. 06 the maximum acceleration occurs for accident situation 3. The accelera-tions in situation 1 and 2 are also in the same scope for both vessels. Furthermore the di�erencesbetween the accelerations within their respective accident situations are not as high as for e.g.Vessel No. 02 or Vessel No. 04. The statistical distribution of the transversal accelerationsin this situation is shown in �gure 4.14.


29

4 Examination

4.8 Vessel No. 08




Lpp 283.20 [m]

B 32.20 [m]

TD 11.00 [m]


Vessel No. 08 has the geometric capacity to carry 5, 041TEU . Having the main dimensionsaccording to table 4.15, it is a typical Panamax container vessel like Vessel No. 04. Thefollowing characteristics of Vessel No. 08 are to be noted:


� The documented bilge keel area is slightly larger than the mean value according to chapter3.9.



As for Vessel No. 04, the �rst analysed Panamax vessel, the cB value is relatively high for acontainer vessel and the GMmin is small. The calculated transversal accelerations on the bridgeand the rolling angles for the three accident conditions are listed in table 4.16.


Accidentsituation

atmax

[m/s2

]ϕmax [◦]

Situation 1 11.0 27

Situation 2 9.0 18

Situation 3 13.0 35

The maximum acceleration occurs for accident situation 3. The distribution of the highestaccelerations on the three accident situations is similar to the distribution of Vessel No. 04,where the highest value also occurs for accident situation 3 while the lowest value occurs forsituation 2. The statistical distribution of the transversal accelerations in this situation is shownin �gure 4.16.

30

4.9 Vessel No. 09


4.9 Vessel No. 09




Lpp 277.00 [m]

B 32.25 [m]

TD 12.20 [m]


Vessel No. 09 has the geometric capacity to carry 4, 318TEU . Having the main dimensionsaccording to table 4.17, it is a typical Panamax container vessel like Vessel No. 04 and VesselNo. 08. Due to its design draft of 12.2m, the vessel is not able to pass the Panama Canal indesign loading condition, because in the canal the draft is limited to 12.04m. Another loadingcondition with a smaller draft has to be chosen for the passage. The following characteristics ofVessel No. 09 are to be noted:

� The lines of the ship shown in �gure 4.17 have a cB value of 0.65 on design draft. Further-more the slanted transom is unusual.

31

4 Examination

� The documented bilge keel area is slightly smaller than the mean value according to chapter3.9.

� The stability in ballast arrival loading condition is less high resulting in the smallest GMof the examination GMsolid = 5.09m.


Like the other Panamax vessels, also Vessel No. 09 has a relatively high cB value and a verysmall GMmin. The calculated transversal accelerations on the bridge and the rolling angles forthe three accident conditions are listed in table 4.18.


Accidentsituation

atmax

[m/s2

]ϕmax [◦]

Situation 1 12.0 38

Situation 2 7.5 22

Situation 3 14.0 35

Until now the maximum transversal acceleration of 14m/s2 in situation 3 is the worst valuecalculated. As for Vessel No. 04 and Vessel No. 08, the highest acceleration value occurs forsituation 3, while the lowest is associated to situation 2. Notable is the fact, that the highestvalue is twice as high as the lowest. The statistical distribution of the transversal accelerationsin this situation is shown in �gure 4.18.


32

4.10 Vessel No. 10

4.10 Vessel No. 10




Lpp 195.40 [m]

B 29.80 [m]

TD 10.10 [m]


Vessel No. 10 has the geometric capacity to carry 2, 478TEU . Having the main dimensionsaccording to table 4.19, it is the smallest analysed vessel. In addition it is the only vessel equippedwith cranes and a deck house located at the ship's aft end. The following characteristics ofVessel No. 10 are to be noted:







Accidentsituation

atmax

[m/s2

]ϕmax [◦]

Situation 1 12.0 32

Situation 2 14.5 43

Situation 3 12.0 36

The maximum acceleration of 14.5m/s2 occurs for accident situation 2 while the associatedrolling angle of 43◦ is the highest calculated value in the whole examination. The statisticaldistribution of the transversal accelerations in this situation is shown in �gure 4.20.

33

4 Examination


4.11 Vessel No. 11




Lpp 322.60 [m]

B 45.60 [m]

TD 13.00 [m]


Vessel No. 11 has the geometric capacity to carry 8, 600TEU . Having the main dimensionsaccording to table 4.21, it is the largest vessel analysed. It belongs to the class of large Post-Panamax vessels. The following characteristics of Vessel No. 11 are to be noted:


� The documented bilge keel area is much larger than the mean value according to chapter3.9.

� The stability in ballast arrival loading condition is extremely high resulting in aGMsolid = 12.96m.

34

4.11 Vessel No. 11


The ship is very �ne with its cB value of 0.59. The stability values GMsolid and mainly GMmin

have a signi�cant higher order of magnitude, than the values of the previous analysed vessels.The calculated transversal accelerations on the bridge and the rolling angles for the three accidentconditions are listed in table 4.22.


Accidentsituation

atmax

[m/s2

]ϕmax [◦]

Situation 1 4.0 11

Situation 2 3.5 8

Situation 3 5.5 12

The maximum acceleration occurs for accident situation 3. But the calculated accelerations areconsiderably smaller than for the previous analysed vessels. The statistical distributionof the transversal accelerations in this situation is shown in �gure 4.22.


35

4 Examination

4.12 Vessel No. 12




Lpp 249.03 [m]

B 32.20 [m]

TD 11.30 [m]


Vessel No. 12 has the geometric capacity to carry 4, 300TEU . Having the main dimensionsaccording to table 4.23, it is another midsized container vessel which may travel through thePanama Canal. The vessel is comparable to Vessel No. 07, which has nearly the samedimensions, a slightly smaller cB value and therefore a �ner hullform as well as a smaller geometricTEU capacity. The following characteristics of Vessel No. 12 are to be noted:


� The documented bilge keel area is signi�cant smaller than the mean value according tochapter 3.9.





Accidentsituation

atmax

[m/s2

]ϕmax [◦]

Situation 1 10.5 25

Situation 2 11.0 26

Situation 3 14.0 35

The maximum acceleration occurs for accident situation 3. The maximum acceleration ishigher, than for the comparable Vessel No. 07. The statistical distribution of the transversalaccelerations in this situation is shown in �gure 4.24.

36

4.13 Vessel No. 13


4.13 Vessel No. 13




Lpp 210.25 [m]

B 30.00 [m]

TD 10.10 [m]


Vessel No. 13 has the geometric capacity to carry 2, 824TEU . Having the main dimensionsaccording to table 4.25, it is the second smallest analysed vessel. The following characteristicsof Vessel No. 13 are to be noted:


� The documented bilge keel area matches the mean value according to chapter 3.9.


37

4 Examination




Accidentsituation

atmax

[m/s2

]ϕmax [◦]

Situation 1 12.0 31

Situation 2 15.0 36

Situation 3 12.5 32

The maximum acceleration occurs for accident situation 2. The transversal acceleration of15m/s2 in accident situation 2 is the highest value that occurs in the scope of the simulations.Mentionable is the fact, that all smaller vessels analysed in this chapter, are critical in accidentsituation 2, while for the other vessels the critical situation is situation 3. Apparently the seawayin situation 2 with a shorter signi�cant wave period of TS = 8.5 s stronger excites the smallvessels. The statistical distribution of the transversal accelerations in this situation is shown in�gure 4.26.


38

4.14 Vessel No. 14

4.14 Vessel No. 14




Lpp 319.00 [m]

B 42.80 [m]

TD 13.00 [m]


Vessel No. 14 has the geometric capacity to carry 8, 600TEU . Having the main dimensionsaccording to table 4.27, it belongs to the class of the large Post-Panamax vessels. With VesselNo. 14 the Chicago Express takes part of the analysis, which is the vessel involved in accidentsituation 1. For the BSU accident report [1] it has already been examined, although referring toa di�erent loading condition. The following characteristics of the Chicago Express are to benoted:


� The documented bilge keel area is a little bit larger than the mean value according tochapter 3.9.

� The stability in ballast arrival loading condition is extremely high resulting in aGMsolid = 12.40m.


Besides Vessel No. 11, the Chicago Express is the second vessel in the examination outof the class of large Post-Panamax vessels. With a cB value of 0.66, the Chicago Expresshas not such a �ne shaped hull as Vessel No. 11. But the stability values GMsolid and mostnotably GMmin also have a signi�cant higher order of magnitude, than the values for the smalleranalysed vessels. The calculated transversal accelerations on the bridge and the rolling anglesfor the three accident conditions are listed in table 4.28.


Accidentsituation

atmax

[m/s2

]ϕmax [◦]

Situation 1 3.0 7

Situation 2 3.5 8

Situation 3 3.0 8

39

4 Examination

The maximum acceleration occurs for accident situation 2. As for the �rst large vessel anal-yse, Vessel No. 11, the calculated accelerations are considerably smaller than for the previousanalysed vessels. Nevertheless in the accident condition of Vessel No. 11, the Chicago Express,the transversal accelerations on the bridge exceeded 1.0 g (refer to BSU investigation report [1])!The statistical distribution of the transversal accelerations in this situation is shown in �gure

4.28.


40

4.15 Vessel No. 15

4.15 Vessel No. 15




Lpp 319.00 [m]

B 42.80 [m]

TD 13.00 [m]


The last analysed vessel has the geometric capacity to carry 8, 200TEU . Having the maindimensions according to table 4.29, it belongs to the large Post-Panamax vessels. The vessel isvery similar to the Chicago Express as it has exactly the same main dimensions as well as anequivalent ballast arrival loading condition. The following characteristics of Vessel No. 15 areto be noted:

� The lines of the ship shown in �gure 4.29 have a cB value of 0.65 on design draft

� The documented bilge keel area is larger than the mean value according to chapter 3.9

� The calculated cross-curves in E4 coincide well with the ones stated in the trim & stabilitybooklet

� The stability in ballast arrival loading condition is extremely high resulting in aGMsolid = 12.49m

� The limiting intact stability criterion (Max. GZ at 25◦) requires a GMmin = 4.77m



Accidentsituation

atmax

[m/s2

]ϕmax [◦]

Situation 1 4.5 11

Situation 2 4.0 8

Situation 3 5.0 11

The maximum acceleration occurs for accident situation 3. Although Vessel No. 15 is verysimilar to the Chicago Express, the accelerations di�er. The statistical distribution of thetransversal accelerations in this situation is shown in �gure 4.30.

41

4 Examination


42

5 Evaluation

Based on the determination of the seakeeping behavior in the previous chapter, the followingsections summarize and explain the results, highlight the consequences and give recommendationsfor further detailed examinations also carried out in the scope of this thesis.

5.1 Results

The examination includes only container vessels, which are altogether rather similar in terms ofhull form and ship design. This is due to the necessity to carry as much containers as possibleon a vessel in combination with relatively high speed requirements (> 20 kts). All vessels have,more or less, a distinctive bow �are and a �ne shaped hull form compared to other ship types(e.g. bulkers or tankers). This is expressed by cB values in a scope of 0.57 ... 0.69.

The results show, that the transversal accelerations on the bridges are correlated with therespective rolling angles. Therewith it is not implied, that one explicit rolling angle alwayscauses one explicit acceleration. But it can be stated, that high accelerations only occur incombination with large rolling angles.

Summing up the results of the examination of the single ships in the ballast arrival loadingcondition reveals:

� In their ballast arrival loading condition all examined ships have, more or less, a GM value,which is signi�cantly higher than the required minimum GMmin according to the rules ofthe IMO[4]. It can be stated, that all vessels considered have a very high stability.

� Most vessels experience large rolling angles up to 40◦ and high transversal accelerations onthe bridge up to 15m/s2, depending on the examined accident situation named in chapter3.12.

To get an overview of the examination, all calculated transversal acceleration on the bridgeagainst their respective GMsolid are plotted in �gure 5.1. The numbers in �gure 5.1 representthe respective vessels in chapter 4. At this, the maximum transversal acceleration is plotted foreach of the three accident situations. For better comparison of the occurring accelerations, twoof the vessels in accident are considered, too. The Chicago Express (abbreviated with CE)and the 2468 TEU Vessel in their respective accidental loading condition are added to thegraph for each of the three analysed accident situations.

43

5 Evaluation

2468 TEU in

accident

CE in accident

10

47

6

5

13 12

8

9

11

15

14 = CE

1

2

3

0

2

4

6

8

10

12

14

16

4 6 8 10 12 14

GMsolid [m]

Tra

nsvers

e a

ccele

rati

on

on

th

e b

rid

ge

in

ball

ast

arr

ival

load

ing

co

nd

itio

n [

m/s

2]

Accident situation 1 Accident situation 2 Accident situation 3

Figure 5.1: Transversal accelerations on the bridge against GMsolid

5.2 Consequences

Normally it is expected that large vessels with a length of over 200m or even 300m are relativelysafe in heavy sea and do not experience an exceptional seakeeping behavior. But the analysisreveals, that most of the considered container vessels apparently have signi�cant problems withtheir seakeeping behavior in combinations of certain loading and environmental conditions.

In exception to the above stated the three largest vessels, namely Vessel No. 11, VesselNo. 14 and Vessel No. 15, experience smaller rolling angles and accelerations during the ex-amination (see �gure 5.1). Simply looking at this result, it could be concluded, that these largevessels generally do not have problems in the considered seaways. But with Vessel No. 14,the Chicago Express takes part of the examination, being the vessel in accident, which is de-scribed with accident situation 1 (refer to table 3.1). During this accident very high rolling anglesand transversal accelerations on the bridge occurred in a di�erent loading condition (compareBSU report [1]).

The examined ballast arrival condition di�ers from the accident loading condition. TheChicago Express now has a smaller displacement and GM as well as a di�erent trim. Thisimplies that the other large vessels, Vessel No. 11 and Vessel No. 15 may also be endangeredto experience equally high high transversal accelerations in a di�erent loading condition. Thisassumption is analysed further in chapter 6.2.

The problems in the seakeeping behavior occur due to the following reasons: The shaped hullform and the signi�cant bow �are of the analysed vessels favours the impact of direct, excitingheeling moments through the heavy sea. On the other hand, the excessive stability causes highrestoring moments of the heeled vessel. This results in signi�cant transversal accelerations (see[8] for more details).

Furthermore the examination shows that the problem of excessive rolling angles and transversal

44

5.3 Recommendations

accelerations seems not to be a pure stability problem. Rather high accelerations occur for awide scope of examined GMsolid values (see �gure 5.1).Regarding the occurring maximum transversal accelerations, a comparison with an usual value

for the dimensioning of the container lashing equipment is interesting, since a reference valuefor the maximum transversal accelerations acting on humans on the bridge does not exist. Forexample according to the DNV rules [12], the transversal dynamic acceleration taking e�ect oncontainer lashings on deck, shall be taken not smaller than ∼ 0, 5 g. The calculated accelerationson the bridge partly exceed the triple of that value. In the same time the normalized mean valueof the occurring acceleration amplitudes mostly exceeds a value of ∼ 0, 5 g (refer to the respectivehistograms in chapter 4). Such high transversal accelerations are considered being de�nitely notacceptable.

5.3 Recommendations

The simulation results show, that the ballast arrival loading condition of container vessels isnot a safe seagoing condition. The risk of encountering excessive rolling angles and very hightransversal accelerations on the bridge in heavy sea is increased signi�cantly. Based on thesimulation results, the following approaches to reduce the risk of accidents can be exempli�ed.

5.3.1 Stability

Concerning the stability of the vessels, no universally valid GM value, which reduces the risk ofaccidents, can be derived from the analysis. The seakeeping behavior of a ship apparently hasa lot of important additional in�uence factors. For instance two of the factors which have tobe considered, are the ship's trim and the hull form. Altogether the factors can form a criticalship situation consisting of the ship's stability, the ship's trim, the ship's hull form and so on.To identify such critical situations for each loading condition, seakeeping calculations have tobe done with adequate methods for each vessel individually. A general prediction of a criticalsituations is not possible until now. For three of the vessels in ballast arrival loading condition,the most critical situation is determined in chapter 6.1.

5.3.2 Roll damping

The enlarging of the roll damping, no matter how the damping is done, reduces the roll motionsand transversal accelerations on the bridge. There are di�erent ways to increase the roll dampingof a ship. According to Abdel-Maksoud [11] the following possibilities �t for this purpose:

� Enlarge the bilge keel area → roll damping by �ow separation at the bilge keels

� Increase the ship's speed at low speeds→ roll damping by shear stress on the hull, angularincoming �ow on the rudder and immersed transom

� Integrate a roll damping tank → roll damping by e.g. a sloshing �uid

For a vessel already in service, the bilge keels could be modi�ed easily. Though such a modi�-cation would not have a deciding in�uence on the transversal accelerations. In appendix B.1 agraph can be found, where the bilge keel area is changed for Vessel No. 13, being the vesselwith the highest occurring transversal acceleration value during the examination. In the graphthe vessel in ballast arrival condition encounters the seaway of accident situation 2. it follows,that the enlarging of the bilge keel area by 50%, just provides a reduction of the transversalaccelerations of about 10%. A general advantage of bilge keel is, that they also function withzero speed.

45

5 Evaluation

Furthermore the increase of the ship's speed always reduces the roll motion. But at �rst thevessel has to be able to signi�cantly increase the speed, which is not self-evident due to the highwave forces slowing the ship with each wave. On the other hand a higher ship's speed in heavyseaway causes high slamming loads on the ship's bow structure, when heading into the waves.This e�ect may cause severe damages on the structure, especially for vessels with a large bow�are. At last with a higher speed and heading into the waves, the vessel may be endangered ofencountering a critical 2:1 resonance. Therefore the augmentation of the ship's speed to improvethe roll damping is suitable to only a limited number of cases. The in�uence of ship's speed isalso determined for Vessel No. 13. The associated graph in appendix C.1 shows that the ship'sspeed has not a signi�cant in�uence, too. For this analysis, the vessel in ballast arrival conditionencounters again the seaway of accident situation 2.At last the integration of a roll damping tank has the advantage, that it also functions with

zero ship's speed. But it reduces the ship's payload due to the used space for the tank andreduces the intact stability due to the free surface of the tank.

5.3.3 Lines of the ship

The design of the lines of the ship has a strong in�uence on the seakeeping behavior. As men-tioned before, the shape of the frames or rather the shape of the bow �are in combination withthe wide transom, governs the induced rolling moments. Already during the very early designphase, the following compromise has to be determined. On one hand the vessel is intended tocarry as much cargo as possible which results in �aring hull forms. On the other hand this oftencontradicts with the demand of a good seakeeping behavior.

5.3.4 Other

The operating behavior of the crew has also an in�uence. Besides the increase of the ship's speed,the risk of accident can be reduced by placing the vessel parallel to the main wave direction atzero speed. In beam sea a lot of the wave energy induced into the ship is transformed into adrift motion in beam direction. Therefore the roll motions of the vessel are reduced. A problemin this position can be, that the ship's stern turns into the waves due to the poor course keepingability at zero speed. When this happens to container vessels with their wide and �at transom,the stern experiences often high slamming loads. Furthermore drifting in beam sea is obviouslynot advisable inshore.

46

6 Detailed examination

The evaluation discussed in chapter 5 discloses, that further investigations are necessary for thebetter understanding of the high transversal acceleration problem. For this reason the followingdetailed examinations are carried out.At �rst, the in�uence of the ship's stability on the transversal accelerations is analysed. Fur-

thermore it has to be examine, if the large vessels, Vessel No. 11 and Vessel No. 15, are alsoendangered to encounter high acceleration and rolling angle values in a loading condition similarto the one of Vessel No. 14 (Chicago Express) when it experienced severe ship motions inaccident.

6.1 Variation of the GM values

In this chapter the in�uence of the initial stability (namely GM) on the occurring transversalacceleration for three out of the 15 examined vessels is determined. In order to consider theprobable in�uence of the ship's size, a small, a mid-sized and a large vessel are chosen.Based on the ballast arrival loading condition, the value of GMsolid is varied by changing the

vertical center of gravity KG of the vessel. The calculations are performed without consideringthe in�uence of free surfaces, for the reasons named in chapter 3.6. The displacement as well asthe ship's trim of the analysed ballast arrival condition are kept constant. For each GM valueall three accident situations according to chapter 3.12 are simulated.In addition it is estimated, if such a GMsolid or respectively KG value is achievable from a

technical point of view. For instance a total ship's center of gravity KG at height of the innerbottom is not realistic. The feasible minimum KG depends on the light ship's vertical center ofgravity, the position and �lling of the ballast water and fuel oil tanks in the lower part of theship as well as cargo in the holds.A shifted GM directly a�ects the seakeeping behavior. Hence to represent well the di�erences,

a new set of transfer functions (RAOs) according to chapter 2.1.1 has to be calculated for eachGM value.

6.1.1 Small vessel

Vessel No. 13 was chosen as smallest vessel for the detailed stability analysis. Its relevant dataare listed in table 6.1. More main dimension data of this vessel can be found in the appendix A.13on page 71. The GM is varied around the ballast arrival GMsolid = 6.98m within a range ofabout GM ∼= 3 ... 12m.In �gure 6.1 the resulting transversal accelerations on the bridge are shown related to the

di�erent GMsolid values. All three accident situations result in a comparable curve slope. Inaccident situation 1 and 2 the highest accelerations occur for the GM value of the ballast arrivalloading condition. In accident situation 3 the highest acceleration occurs for a higher GM ofabout 8m. With a higher or a lower stability the vessel would experience signi�cantly smalleraccelerations. Though just a GMsolid value of 8 ... 9m is realistically reachable for this vessel bye.g. �lling ballast water in tanks in low positions. Higher values in this simulation can only bereached by decreasing the vertical center of gravity of the lightship weight, which is consideredbeing impossible for an existing vessel.

47


Table 6.1: Stability data for the small vessel

Ballast arrival loading

conditionValue Unit

KM 15.46 [m]

KG 8.48 [m]

GMsolid 6.98 [m]

Light ship Value Unit

vcgLSW 12.18 [m]

Ba

llast a

rriv

al lo

ad

ing

co

nd

itio

n

0

2

4

6

8

10

12

14

16

2 4 6 8 10 12 14 16

GMsolid [m]

Maxim

um

tra

nsvers

e a

ccele

rati

on

on

th

e b

rid

ge [

m/s

2]


Figure 6.1: Vessel No. 13 in ballast arrival �oating condition: Variation of GMsolid

6.1.2 Midsized vessel

The midsized vessel for the detailed stability analysis is Vessel No. 1. Its relevant data are listedin table 6.2. More main data of this vessel can be found in the appendix A.1 on page 59. The GMis varied around the ballast arrival GMsolid = 10.43m within a range of about GM ∼= 5 ... 13m.

In �gure 6.2 the resulting transversal accelerations on the bridge are shown related to thevaried GMsolid values. All three accident situations result in a comparable curve slope. Onaverage the highest accelerations occur for a GM in the range of the GMsolid within the ballastarrival loading condition. It is very mentionable, that the vessel would also experience lowertransversal accelerations on the bridge, even when the stability is further increased. Though justa GMsolid value of about 11m is realistically reachable for this vessel by e.g. �lling tanks inlow positions. Again, higher GM values are only realisable by changing the vertical center ofgravity of the lightship weight. When reducing the stability by decreasing GM , the transversal

48

6.1 Variation of the GM values

accelerations also decrease signi�cantly to values of about 3m/s2.

Table 6.2: Stability data for the midsized vessel


conditionValue Unit

KM 21.45 [m]

KG 11.02 [m]

GMsolid 10.43 [m]


vcgLSW 15.13 [m]

Ba

llast a

rriv

al lo

ad

ing

co

nd

itio

n

0

2

4

6

8

10

12

14

16

2 4 6 8 10 12 14 16

GMsolid [m]

Maxim

um

tra

nsvers

e a

ccele

rati

on

on

th

e b

rid

ge [

m/s

2]


Figure 6.2: Vessel No. 01 in ballast arrival �oating condition: Variation of GMsolid

6.1.3 Large vessel

The large vessel for the detailed stability analysis is the Chicago Express. Its relevant dataare listed in table 6.3, while more detailed data can be found in the appendix A.14 on page 72.The GM is varied around the ballast arrival GMsolid = 12.40m in both directions within a rangeof about GM ∼= 5 ... 15m.

In �gure 6.3 the resulting transversal accelerations on the bridge are shown related to thevaried GMsolid values. For all three accident situations it follows a comparable curve slope. Thistime no signi�cant transversal accelerations occur in the ballast arrival loading condition. Witha higher stability, than in the ballast arrival loading condition, the behavior of the vessel doesnot change. Furthermore all analysed GMsolid values up to 14m are realistically reachable for

49


this vessel by e.g. �lling ballast water in tanks in low positions. When reducing the GM of theballast arrival loading condition, the transversal accelerations increase signi�cantly up to 10m/s2

for a GM around 8.5m. Then they go down again to uncritical accelerations around 2m/s2.

Mentionable is the fact, that the accident of the Chicago Express occurred in a loadingcondition with the same GM = 8.54m. (refer to BSU report [1]).

Table 6.3: Stability data for the large vessel


conditionValue Unit

KM 25.64 [m]

KG 13.24 [m]

GMsolid 12.40 [m]


vcgLSW 15.62 [m]

Ba

llast

arr

iva

l lo

ad

ing

co

nd

itio

n

0

2

4

6

8

10

12

14

16

2 4 6 8 10 12 14 16

GMsolid [m]

Maxim

um

tra

nsvers

e a

ccele

rati

on

on

th

e b

rid

ge [

m/s

2]


Figure 6.3: Chicago Express in ballast arrival �oating condition: Variation of GMsolid

6.1.4 Comparison of the simulation results

In �gure 6.4 the curves of the three vessels are compared for the accident situation 1. For theother accident situations, the curve shape is comparable. It can be identi�ed, that each vessel hasa unique critical condition, where an exciting seaway in combination with the ship's hull form,the ship's trim and the GM value, result in very high transversal accelerations on the bridge.

50

6.2 Rolling behavior of the large vessels

0

2

4

6

8

10

12

14

16

2 4 6 8 10 12 14 16

GMsolid [m]

Maxim

um

tra

nsvers

e a

ccele

rati

on

on

th

e b

rid

ge [

m/s

2]

Small Vessel no.13 Midsized Vessel No.01 Large Vessel No.14 = CE

Figure 6.4: Comparison of the stability in�uence for the three vessels in accident situation 1


As mentioned in chapter 5.2 the large vessels, analysed in the ballast arrival loading condition,Vessel No. 11, Vessel No. 14 (Chicago Express) and Vessel No. 15 neither experiencehigh rolling angles nor high transversal accelerations on their bridges. But the Chicago Ex-press is de�nitely endangered to experience very high transversal accelerations, as e.g. whenit encountered accident situation 1 and high transversal accelerations of up to 10m/s2 occurred(refer to BSU report [1]). The data of the loading condition during the accident is shown intable 6.4. Therefore it is presumed, that the other two large vessels also reach high transversalaccelerations, when they operate in such a loading condition. This presumption shall examinedin the following.

For this reason the seakeeping behavior of the two other large vessels is determined for several ofsuch comparable loading conditions. To achieve more clarity, the results of this investigation areonly shown for accident situation 1, being the Chicago Express accident situation. (comparesection 3.12)

51


Table 6.4: Loading condition of the Chicago Express during its accident

Main

dimensionsValue Unit

4 66649 [t]

TAP 9.07 [m]

TFP 7.08 [m]

Trim -1.99 [m]

KM 23.36 [m]

KG 14.82 [m]

GMsolid 8.54 [m]

6.2.1 Large Vessel No. 15

Firstly Vessel No. 15 is analysed, of which the main dimensions can be found in appendix A.15.This vessel is very similar to the Chicago Express (CE) in its main dimensions and hull form.The �oating condition which is set for the investigation is shown in table 6.5. The KG andtherefore the GMsolid are varied in the scope of the GMsolidCE of the Chicago Express duringthe accident, while the displacement, the drafts and the trim are kept constant. These valuescomply with the displacement, drafts and trim from the Chicago Express in its accident.

Subsequently the seakeeping behavior is determined for this compilation of loading conditions,consisting of the mentioned �oating condition and a varied GM value.

Table 6.5: Vessel No. 15: CE alike �oating condition

Main


4 66649 [t]

TAP 9.19 [m]

TFP 7.20 [m]

Trim -1.99 [m]

KM 23.19 [m]

KG variable [m]

GMsolid variable [m]

Table 6.6 speci�es the resulting transversal accelerations on the bridge and the respectiveGMsolid values in accident situation 1. The GMsolid is randomly varied in the analysed scope.The associated curve is shown in �gure 6.5. For comparison, the transversal acceleration accord-ing to the GMsolidCE for the Chicago Express in its accident loading condition is included inthe �gure.

The results prove the initial hypothesis to be correct. Vessel No. 15 is also endangered tosu�er high transversal acceleration on its bridge in a slightly di�erent loading condition, thanthe ballast arrival loading condition.

52


Table 6.6: Vessel No. 15: Transversal accelerations for CE alike loading conditions

Loading

conditions

GMsolid

[m]atmax[m/s2

]CE Accident 8.54 10.0

no. 15 V1 6.05 2.5

no. 15 V2 7.79 9.5

no. 15 V3 9.05 7.0

no. 15 V4 9.78 6.5

no. 15 V5 10.72 5.5

no. 15 V6 11.66 5.0

0

2

4

6

8

10

12

5 6 7 8 9 10 11 12

GMsolid [m]

Maxim

um

tra

nsvers

e a

ccele

rati

on

on

th

e b

rid

ge [

m/s

2]

Vessel No.15 in CE accident condition CE in accident

Figure 6.5: Vessel No. 15: Variation of GMsolid in CE alike loading condition

6.2.2 Large Vessel No. 11

Subsequently Vessel No. 11 is analysed in the same way. Its main dimensions can be found inappendix A.11. The �oating condition shown in table 6.7 is set for Vessel No. 11. The KGand therefore the GMsolid are again randomly varied in the range of GMsolidCE of the ChicagoExpress during the accident. The displacement, drafts and trim in this �oating condition arekept constant. They also comply with the values of the Chicago Express in its accident .

The resulting compilation of loading conditions, consisting of the mentioned �oating conditionand a varied GMsolid value, is then used to determine the respective seakeeping behavior.

53


Table 6.7: Vessel No. 11: Chicago Express alike �oating condition

Main


4 66649 [t]

TAP 9.07 [m]

TFP 7.08 [m]

Trim -1.99 [m]

KM 24.30 [m]

KG variable [m]


The results listed in table 6.8 show, that Vessel No. 11 at �rst does not experience excessivetransversal accelerations . However for GMsolid = 9.28m a slightly maximum for the transversalacceleration of 5.5m/s2 is already considered to be noticeable. So for this speci�c sea conditionwithin accident situation 1, a GMsolid value of about 9m leads to the highest, but insigni�cantaccelerations.

Table 6.8: Vessel No. 11: Transversal accelerations for CE alike loading conditions

Loading

conditions

GMsolid

[m]atmax[m/s2


no. 11 V1 6.28 3.5

no. 11 V2 8.02 4.5

no. 11 V3 9.28 5.5

no. 11 V4 10.01 5.0

no. 11 V5 10.95 5.0

no. 11 V6 11.89 5.0

Following from this result, another compilation of displacement, trim and GM should bedetermined, where the constant excitation of the seaway results in high accelerations. For thisreason the vessel is immersed slightly deeper. The new �oating condition shown in table 6.9 isset. A new compilation of loading conditions is then created by varying GM in the same scopeas before.

Table 6.9: Vessel No. 11: New �oating condition

Main

dimensions

Value Unit

4 80,000 [t]

TAP 10.68 [m]

TFP 8.69 [m]

Trim -1.99 [m]

KM 23.53 [m]

KG variable [m]


The results listed in table 6.10 show, that Vessel No. 11 in accident situation 1 now expe-

54


riences signi�cant higher transversal accelerations on the bridge up to 10m/s2, than within theloading condition summarized in table 6.7. As in the CE alike loading condition, the maximumvalue occurs for a GMsolid of about 9m. The associated curves for both loading conditions areshown in �gure 6.6. For comparison, the situation of the Chicago Express in its accidentloading condition is also shown.The results prove the given presumption for Vessel No. 11 to be correct, too. A rather slight

variation of the �oating condition leads the vessel to the risk of experiencing very high transversalaccelerations on its bridge. Therefore all vessels, including the large vessels have an increasedrisk of accident in the examined seaways.

Table 6.10: Vessel No. 11: Transversal accelerations for new loading conditions

Loading conditionGMsolid

[m]atmax[m/s2


no. 11 V7 6.23 3.5

no. 11 V8 7.97 5.5

no. 11 V9 9.24 10.0

no. 11 V10 9.96 8.0

no. 11 V11 10.90 7.0

no. 11 V12 11.84 6.0

0

2

4

6

8

10

12

5 6 7 8 9 10 11 12

GMsolid [m]

Maxim

um

tra

nsvers

e a

ccele

rati

on

on

th

e b

rid

ge [

m/s

2]

Vessel No.11 in CE accident condition Vessel No.11 in new condition CE in accident

Figure 6.6: Vessel No. 11: Variation of GMsolid in di�erent loading conditions

In addition, the curves in �gure 6.6 con�rm the statement, already given in chapter 5.2. Thisexamination clearly shows, that the problem of high accelerations on the bridge is de�nitely nota pure stability problem. Here the di�erences between the two loading condition sets, listed

55


in tables 6.7 and 6.9, are a higher displacement and therefore a higher draft of about 1.6mfor the second loading condition set. For a vessel of this size, these di�erences do not seemremarkable. Nevertheless for one of the �rst loading conditions, a moderate maximum transversalacceleration of 5.5m/s2 occurs, while for one of the second loading conditions, the value becomessigni�cantly higher, reaching an extremum of 10m/s2. These maximum accelerations occur for aGMsolid

∼= 9.25m in both cases.The analysis reveals that signi�cantly di�erent accelerations may occur for similar GM values

and just slightly di�erent �oating conditions. Thus a simple way to decrease the risk of accidents,like the determination of a single upper limit for the GM for example, to limit the excessivestability and decrease the occurring transversal accelerations is not a feasible approach.

56

7 Conclusions

Summing up the results from the thesis can be done by stating: All examined container vesselshave a signi�cant problem with their seakeeping behavior in the ballast arrival loading condition.Within this examination, all vessels reach very high transversal accelerations on their bridges.This problem with excessive accelerations occurs for loading conditions, where the vessels haveno or only few cargo on board resulting in rather small drafts and thus high stability values. Fortwelve of the analysed vessels the ballast arrival loading condition is most critical while for thethree largest vessels the most critical condition occurs at higher drafts at the FP.Further, this thesis proves that the named problem is not caused by the high stability values

only. Other factors like the ship's trim or the ship's hull form also have a great in�uence on theseakeeping behavior. Therefore a simple approach like the determination of a single upper limitfor the GM does not seem to be a feasible approach to avoid such accidents in the future.Particularly due to distinctive nonlinear e�ects, mainly on the roll motion, the seakeeping

behavior can de�nitely not be calculated with simple linear approaches. Therefore it is rec-ommended, that the seakeeping behavior for each single loading condition should be evaluatedduring the early design process by the application of numerical methods, which are capable tosimulate these nonlinearities. In this way it can be identi�ed, whether a ship's ballast arrivalloading condition should be stated to be a seagoing condition or if there is an increased riskof accident. With such methods, it is possible to reproduce the behavior of the ships duringreal accidents very well (refer to the accident reports [1][2][3]). Thus the seakeeping calculationsperformed for this thesis, also represent well the real seakeeping behavior of the analysed vesselsand are adequate to estimate the risk of encountering an accident.Having gained this knowledge, it becomes obvious that there is a need for establishing manda-

tory regulations for the determination of the seakeeping behavior and to increase the safety onthe bridges for the crew.Furthermore, since the excessive stability alone is not responsible for the accidents, the oper-

ating could be considered as main cause. This is not reasonable, because the crew of all vesselswithin the analysed accident situations [1][2][3] followed a good seamanship for the behaviourin heavy seas. This behavior, which consists mainly of heading into the waves at slow speeds,is the result of long lasting experiences on vessels in heavy sea. Following this procedure it isensured, that vessels keep their manoeuvrability and do not face high slamming loads on thebow structure as well as green water on deck. These e�ects can cause severe damages on theship's hull structure and on the stowed containers on deck.Concluding, it has to be stated, that container vessels facing the described circumstances

generally have a highly increased risk of encountering accidents and it is strongly recommendedto perform reliable calculations during the ship design and the approval process in order toidentify operational constraints and thus prevent probable accidents.

57

7 Conclusions

58

A Vessel data

A.1 Vessel No. 01

Table A.1: Detailed main dimensions, Vessel No. 01

General main dimensions Symbol Value Unit

Length over all Loa 274.60 [m]

Length between perpendiculars Lpp 263.00 [m]

Breadth B 40.00 [m]

Depth to freeboard deck D 24.20 [m]

Design draft TD 12.00 [m]

Full scantling draft TFS 14.00 [m]

Lightship weight LSW 23110 [t]

Displacement at TD 4design 73792 [t]

Block coe�cient at TD cB 0.57 -

Service speed vS 26.6 [kts]

Number of containers - 5512 [TEU ]

Maximum ballast water capacity - 14349[m3]

Total bilge keel area ABK 42.50[m2]

Height of the bridge above baseline - 46.50 [m]

Ballast arrival condition data Symbol Value Unit

Ballast arrival displacement 4BallArr 37276 [t]

Used water ballast capacity - 12077[m3]

Draft at after perpendicular TAP 9.05 [m]

Draft at forward perpendicular TFP 4.87 [m]

Trim (negative trimming aftwards) - -4.18 [m]

Height of bridge above ballast arrival waterline - 36.1 [m]

Vertical center of gravity a. B.L. KG 11.02 [m]

Metacentric height without free surface corr. GMsolid 10.43 [m]

Minimum metacentric height GMreq. 1.89 [m]

Limiting intact stability criterion acc. to IMO max. GZ at 25◦

59

A Vessel data

A.2 Vessel No. 02





Breadth B 40.00 [m]























60

A.3 Vessel No. 03

A.3 Vessel No. 03





Breadth B 40.00 [m]























61

A Vessel data

A.4 Vessel No. 04





Breadth B 32.26 [m]






















Limiting intact stability criterion acc. to IMO Area (30, 40) = 0.030m · rad

62

A.5 Vessel No. 05

A.5 Vessel No. 05





Breadth B 32.20 [m]























63

A Vessel data

A.6 Vessel No. 06





Breadth B 32.25 [m]























64

A.7 Vessel No. 07

A.7 Vessel No. 07





Breadth B 32.20 [m]























65

A Vessel data

A.8 Vessel No. 08





Breadth B 32.20 [m]























66

A.9 Vessel No. 09

A.9 Vessel No. 09





Breadth B 32.25 [m]























67

A Vessel data

A.10 Vessel No. 10





Breadth B 29.80 [m]























68

A.11 Vessel No. 11

A.11 Vessel No. 11





Breadth B 45.60 [m]























69

A Vessel data

A.12 Vessel No. 12





Breadth B 32.20 [m]























70

A.13 Vessel No. 13

A.13 Vessel No. 13





Breadth B 30.00 [m]























71

A Vessel data

A.14 Vessel No. 14





Breadth B 42.80 [m]























72

A.15 Vessel No. 15

A.15 Vessel No. 15





Breadth B 42.80 [m]























73

A Vessel data

74

B Variation of the bilge keel area

0

2

4

6

8

10

12

14

16

18

20 25 30 35 40 45 50 55 60 65 70

Bilge keel area [m2]

Maxim

um

tra

nsvers

e a

ccele

rati

on

on

th

e b

rid

ge [

m/s

2]

Vessel No.13 Original value Vessel No. 13

Figure B.1: Vessel No. 13 in ballast arrival loading condition; Variation of the bilge keel area;Accident situation 2

75

B Variation of the bilge keel area

76

C Variation of the ship's speed

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12

Ship's speed [kts]

Maxim

um

tra

nsvers

e a

ccele

rati

on

on

th

e b

rid

ge [

m/s

2]

Vessel No.13 Accident situation 1 & 2 Accident situation 3

Figure C.1: Vessel No. 13 in ballast arrival loading condition; Variation of ship's speed; Seaconditions of accident situation 2

77

C Variation of the ship's speed

78

Bibliography

[1] BSU; Federal Bureau of Maritime Casualty Investigation (2009): Untersuchungsbericht510/08 Tödlicher Personenunfall an Bord des CMS CHICAGO EXPRESS

[2] BSU; Federal Bureau of Maritime Casualty Investigation: Report will be published in 2011;see www.bsu-bund.de for more information

[3] BSU; Federal Bureau of Maritime Casualty Investigation: Report will be published in 2011;see www.bsu-bund.de for more information

[4] IMO; International Maritime Organisation (2002): Code on Intact Stability; ISBN 92-801-5117-7

[5] Söding, H. (1982): Gutachten über die Belastung des Schi�es E.L.M.A. Tres durch Seegangam Vormittag des 26.11.1981; Schrift Nr. 2327 Institut für Schi�bau Universität Hamburg

[6] Kröger, P. (1987): Simulation der Rollbewegung von Schi�en im Seegang; Bericht Nr.473 Institut für Schi�bau Universität Hamburg

[7] Krüger, S. and others (2010): Stability Accidents in Ballast/Laid-Up Conditions - A newphenomenon?; Conference paper for PRADS conference 2010

[8] Kluwe, F. (2009): Development of a Minimum Stability Criterion to Prevent Large Am-plitude Roll Motions in Following Seas; Bericht Nr. 648 Schriftenreihe Schi�bau; ISBN978-3-89220-648-4

[9] Blume, P. (1979): Experimentelle Bestimmung von Koe�zienten der wirksamen Rolldämp-fung und ihre Anwendung zur Abschätzung extremer Rollwinkel; Schi�stechnik Band 26

[10] GRIM, O. (1961): Beitrag zu dem Problem der Sicherheit des Schi�es im Seegang; 316.Mitteilung der Hamburgischen Schi�bau-Versuchsanstalt; Schi� und Hafen 1961 Heft 6

[11] Abdel-Maksoud, M. (2010): Skriptum zur Vorlesung Seeverhalten von Schi�en; Tech-nische Universität Hamburg-Harburg

[12] DNV; Det Norske Veritas (2010): Rules for classi�cation of ships July 2010; Pt.5 Ch.2 Sec.6G300

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