Examination of the intact stability and the seakeeping behaviour

Dezember 2010 

SCHRIFTENREIHE SCHIFFBAU 

Nicolas Rox 

Examination of the intact stability and 

the seakeeping behaviour of container 

vessels within the ballast condition

DIPLOMARBEIT 

für Herrn cand. arch. nav. Nicolas Rox 

Matr.-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 2010 

Abgabe 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 krueger@tu-harburg.de 

Inst. für Entwerfen von Schiffen und Schiffssicherheit Fax: www.ssi.tu-harburg.de 

Schwarzenbergstraße 95, Gebäude C ++49 (40) 428 78 - 6139 

D - 21073 Hamburg

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

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

December 2010

I hereby declare and conrm that this thesis is entirely the result of my own work. I did not 

utilise any other sources and appliances than those specied in the bibliography.

Contents 

List of Figures 

List of Tables 

V 

VII 

1 Introduction 1 

1.1 Key data of the three examined accidents . . . . . . . . . . . . . . . . . . . . . . 1 

1.1.1 Accident of the CMS Chicago Express [1] . . . . . . . . . . . . . . . . 1 

1.1.2 Accident of a 2468 TEU container vessel [2] . . . . . . . . . . . . . . . . 2 

1.1.3 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 . . . . . . . . . . . . . 5 

2.1.1 Linear strip method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 

2.1.1.1 Calculation model . . . . . . . . . . . . . . . . . . . . . . . . . . 5 

2.1.1.2 Roll radius of inertia and roll period . . . . . . . . . . . . . . . . 6 

2.1.1.3 Roll damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 

2.1.1.4 Calculation settings . . . . . . . . . . . . . . . . . . . . . . . . . 7 

2.1.1.5 Typical RAOs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 

2.1.2 Nonlinear seakeeping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 

2.1.2.1 Roll motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 

2.1.2.2 Surge Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 

2.1.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 

2.2 Environmental conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 

2.2.1 Sea condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 

2.2.2 Wind condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 

3 Data input 13 

3.1 Main Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 

3.2 Lines of the ship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 

3.3 Lateral areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 

3.4 Lightship distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 

3.5 Loading condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 

3.6 Free surface correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 

3.7 Intact stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 

3.8 Cross-curves of stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 

3.9 Bilge keel dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 

3.10 Bridge height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 

3.11 Size range of the examined vessels . . . . . . . . . . . . . . . . . . . . . . . . . . 18 

3.12 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 

A.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


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

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

2.3 Jonswap spectrum for H 1/3 = 7, 5 m and T p = 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 GM solid . . . . . . . . . . . . . . . 44 

V


6.1 Vessel No. 13 in ballast arrival oating condition: Variation of GM solid . . . . 48 

6.2 Vessel No. 01 in ballast arrival oating condition: Variation of GM solid . . . . 49 

6.3 Chicago Express in ballast arrival oating condition: Variation of GM solid . . 50 

6.4 Comparison of the stability inuence for the three vessels in accident situation 1 51 

6.5 Vessel No. 15: Variation of GM solid in CE alike loading condition . . . . . . . 53 

6.6 Vessel No. 11: Variation of GM solid in dierent loading conditions . . . . . . . 55 

B.1 Vessel No. 13 in ballast arrival loading condition; Variation of the bilge keel 

area; Accident situation 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 

C.1 Vessel No. 13 in ballast arrival loading condition; Variation of ship's speed; Sea 

conditions of accident situation 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 

VI


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


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

A.1 Detailed main dimensions, Vessel No. 01 . . . . . . . . . . . . . . . . . . . . . . 59 















VIII

Nomenclature 

Symbol Unit Meaning 

A BK 

[ 

m 

2 ] Total bilge keel area 

a t max [ m /s 2 ] Maximum occurring transversal acceleration 

B [m] Ship's breadth 

c B [−] Block coecient 

D [m] Depth to freeboard deck 

△ [t] Displacement of the ship 

g [ m /s 2 ] Gravitational acceleration which is 9.81 m /s 2 

GM corrected [m] Metacentric height with free surface correction 

GM solid [m] Metacentric height without free surface correction 

GZ [m] Righting lever 

H 1/3 [m] Signicant wave height 

KG [m] Vertical center of gravity 

L OA [m] Length over all 

L P P [m] Length between the perpendiculars 

ϕ max [ ◦ ] Maximum occurring rolling angle 

T D [m] Design draft 

T P [s] Peak wave period 

T S [s] Signicant wave period 

v [kts] Ship's speed 

Abbreviation 

Meaning 

a. B.L. above baseline 

AP 

After Perpendicular 

BSU 

Bundesstelle für Seeunfalluntersuchung; Federal Bureau of Maritime 

Casualty Investigation 

DNV Det Norske Veritas 

E4 

A method database for ship design 

FP 

Forward Perpendicular 

HSVA Hamburgische Schibau- Versuchs Anstalt 

IMO 

International Maritime Organisation 

PRADS International symposium on PRActical Design and other oating 

Structures 

RAO Response Amplitude Operator 

TEU 

Twenty feet Equivalent Unit 

TUHH Technische Universität Hamburg-Harburg; Hamburg University of 

Technology 

IX


X

1 Introduction 

In the years 2008/2009 the world economic crisis caused a reduction in the number of transported 

TEU, due to a signicant decrease in transported goods. Consequently a great number of container 

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 vertical 

center of gravity is even located below the lightship condition's coordinate. This is due to large 

amounts of ballast water in wing and double bottom tanks as well as no or only a small amount 

of cargo located at cargo hold bottom. The high amount of ballast water is needed to obtain an 

adequate hull and propeller immersion as well as a limitation of the longitudinal bending moments 

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, several 

accidents have happened to container vessels during the last years. The accidents caused not only 

severe damages on ships but also heavily injured and even killed crew members. They have been 

thrown through the bridge due to high transversal accelerations caused by heavy roll motions 

of the ship. This highlights, that modern container ship designs face some problems concerning 

insucient seakeeping behavior. Since several accidents have happened to ships sailing under 

German ag, the BSU analyzed them by default. For three of the accidents, the seakeeping 

behavior has been examined in detail by order of the BSU at the institute of ship design 

and ship safety at the Hamburg University of Technology (TUHH) [1][2][3]. This 

thesis shall examine the seakeeping behavior of several typical container vessels in equivalent 

environmental conditions. 

1.1 Key data of the three examined accidents 

The examinations revealed signicant parallels between the accidents. They all happened under 

comparable environmental and loading conditions. 

ˆ All ships followed the standard procedure for heavy weather. This means, that they head 

into the sea at slow speeds to minimize the risk of damaging the ship's bow structure due 

to high slamming forces and green water on deck. 

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

ˆ Due to the excessive stability and the therefore short roll periods of the ships, the high roll 

angles resulted in transversal accelerations of up to 14 m /s 2 . 

In the following, an overview of the environmental conditions and several ship data for the 

three examined accidents is given. More detailed information about the accidents and their 

circumstances may be extracted from the respective investigation reports. 

1.1.1 Accident of the CMS Chicago Express [1] 

ˆ The accident happened on September 24th, 2008 during heavy weather in the South 

China Sea near Hong Kong. 

1


ˆ During the accident the waves had a signicant period of approximately T S = 9 ... 10 s and 

a signicant wave height of H 1/3 = 7.5 m. 

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

from astern). 

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

ˆ The ship was lightly loaded, which resulted in KG = 15.647 m (free surface correction 

included) and GM corrected = 7.712 m. 

ˆ The maximum rolling angle was about 35 ◦ . 

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

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

ˆ No noticeable damages to the vessel's hull. 

1.1.2 Accident of a 2468 TEU container vessel [2] 

ˆ The accident happened on September 15th, 2009 during heavy weather in the South 

China Sea near Hong Kong. 

ˆ During the accident the waves had a signicant wave period of T S = 8 ... 9 s and a signicant 

wave height of about H 1/3 = 7 m. 

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

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

ˆ The ship was lightly loaded which resulted in KG = 9.696 m (free surface correction 


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



ˆ One crew member was killed. 

ˆ Heavy damages to the vessel's hull occurred. 

1.1.3 Accident of a 2500 TEU container vessel [3] 

ˆ The accident happened on October 16th, 2009 during heavy weather in the North Sea 

near Borkum. 

ˆ During accident the waves had a signicant wave period of T S = 9 ... 10 s and a signicant 

wave height of about H 1/3 = 7 m. 

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

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

ˆ The ship was lightly loaded which resulted in KG = 10.45 m (free surface correction 


2

1.2 Following objectives for the diploma thesis 



ˆ One crew member was heavily injured. 

ˆ 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 and 

accelerations 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 ballast 

arrival loading condition matches the loading condition of the ships in accident best. In this 

loading condition the ship operates without cargo, with 10 % bunker and stores as well as enough 

ballast water for sucient immersion of the hull. The propeller has to be immersed for adequate 

propulsion. Additionally the fore ship has to be immersed suciently to reduce slamming forces 

on 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 allowed 

bending 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 ballast 

arrival 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 specic ship type. 

For this reason a larger number of container vessels of various size is analysed in the ballast 

arrival loading condition . The goal is to determine the seakeeping behavior for each vessel when 

it is encountering the three aforementioned accident situations. So the maximum rolling angle 

and the maximum transversal acceleration on the bridge are calculated, to estimate the risk 

of accident. All needed calculations are performed with the ship design software E4, which is 

available at Hamburg University of Technology (TUHH). A detailed description of the 

utilised methods can be found in chapter 2. In addition approaches to reduce the risk of accident 

shall be provided, examined and evaluated. 

3


4

2 Theory 

2.1 Description of the utilised seakeeping simulation method 

For the determination of the seakeeping behavior, E4 includes a simulation method developed 

by Söding in connection with the investigation of the capsizing accident of the E.L.M.A Tres 

in 1987 [5]. The method has been further developed by Kröger [6] and in the scope of several 

research projects at the TUHH which led to the actual seakeeping method E4ROLLS. The 

following explanations are based on Krüger [7], Kluwe [8] and the investigation reports of 

the 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 briey 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 six 

RAOs applies for one vessel's speed. Therefore one set of RAOs has to be calculated for each 

speed 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 the 

amplitudes of these four motions stay moderate and that the hydrodynamic inuences outweigh 

the nonlinearities. Therefore it is adequate to incorporate them linearly. Due to the linearisation 

of the sway and yaw motion, the method is not able to describe broaching in following sea, which 

often causes high roll motions and implicates an enhanced danger of capsizing. For the same 

reason the method overestimates the ship's motions in beam seas at low speeds. This is related 

to 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 analysed 

vessel. The cuboid and the ship have equivalent mass moments of inertia. Its height and 

width 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 the 

roll period are calculated. The roll period applies for still water condition and small rolling 

angles. For the roll radius of inertia two values are calculated based on the ship's weight with 

and without the inuence of section added masses, which consider the inuence of the water, 

surrounding the ship's hull. Normally the roll radius of inertia with the inuence of section added 

masses shall not exceed values of about 0.45 B for container vessels. 

For the examined vessels in ballast arrival loading condition, the dry roll radius of inertia 

reaches a value between 0.33 B ... 0.37 B . The wet roll radius of inertia reaches values between 

0.40 B ... 0.42 B. So the used models are reasonable. The estimated roll periods reach values 

between 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 resonance 

condition. This indicates that the assumption of a correct roll damping is mandatory. The 

direct, theoretical calculation of the roll damping is not possible until now. Only the damping 

due to wave radiation can be calculated with potential theory methods. But there are many 

other highly nonlinear and also viscous eects to consider. 

6


For this reason Blume [9] developed roll damping coecients, based on practical experiments 

of ships in model scale. With these empirical coecients the roll damping can be corrected to a 

more realistic value. At this the correction includes also the damping inuence of the bilge keels. 

The roll damping in E4ROLLS is considered with these coecients 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 the 

surge, sway and yaw motion RAOs, which are reaching disproportionately high values or become 

singular. 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 examined 

vessels. In the graphs the RAOs are plotted against the wavelength. Each curve represents one 

encounter 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 dierently. For instance 

the link to the linear motions or the exciting hydrodynamic forces and moments for the roll 

motion 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 to 

be 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 corresponding 

to GM. It is easy to understand, that such a simplication is not permissible. Therefore the 

roll and the surge motion are simulated nonlinearly in the time domain, based on the formulas 

described 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 shown 

below: 

¨ϕ = 

[( ) ( ) ] ( 

I xz ¨ψ + ψ ϕ˙ 

2 cos ϕ − ¨ϑ + ϑ ϕ˙ 

2 sin ϕ − m g − ¨ζ 

) 

h s 

I xx − I xz (ψ sin ϕ + ϑ cos ϕ) 

+ M W ind + M Sway&Y aw + M W ave + M T ank − M D 

I xx − I xz (ψ sin ϕ + ϑ cos ϕ) 

(2.1) 

with 

ˆ 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. 

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

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

ˆ M W ind , M Sway&Y aw , M W ave and M T ank , the exiting roll moments due to wind, sway and 

yaw, waves and uid in tanks or ooded compartments. 

ˆ M D , the nonlinear damping moment depends on ship's speed. It is determined by using 

damping coecients according to Blume [9]. 

ˆ I xx and I xz 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 timeconsuming 

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 using 

Grim'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 added 

hydrodynamic mass) and surge-inducing wave forces. The wave force is calculated, assuming a 

hydrostatic 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 at 

half draught. The surge motion is simulated based on the approach 2.2 below. 

[ 2R (v0 ) R (v o ) 

¨ξ = − ˙ξ + 

v 0 m ∗ v0 2 ξ˙ 

2 + △R ] 

m∗ m ∗ (2.2) 

with 

ˆ R, representing the resistance curve in still water conditions 

9

2 Theory 

ˆ △R, the added resistance due to waves 

ˆ v 0 , the ship's mean speed 

ˆ 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 projects 

at the TUHH including extensive model test at the HSVA. In addition the accident examination 

reports [1][2][3] prove, that it was possible to anticipate exactly the seakeeping behavior of the 

vessels in the respective accident situations. 

Due to the application of Grim's [10] equivalent wave, the method computes reasonably 

fast. Therefore it is possible to obtain realistic results for the seakeeping behavior of ships in 

various seaways within short calculation time. For the same reasons, the method has the named 

limitations of simulating the seakeeping behavior in beam seas and of describing the broaching 

in following seas. Considering these limitations, it is a very suitable method to calculate head 

and 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 waves 

in this seaway have just one direction and a constant wave period. Such seaways do not exist 

in nature and can only be generated in a model tank. Natural seaways are usually represented 

by superposed regular waves of dierent frequencies and encounter directions. A frequency 

distribution appearing in nature is respected by applying a wind sea spectrum like the Pierson- 

Moskowitz 1 or the Jonswap 2 spectrum. These spectra are based on extensive measurements 

of real seaways. The encounter directions are calculated randomly according to a manually chosen 

number of directions. This leads to a more realistic, random seaway with either short-crested or 

long-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 the 

actual wind and a swell part, remaining from former wind conditions. Hence for examinations 

in seaways containing a high swell part, it may be reasonable to generate a seaway based on a 

so 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 the 

seaway. 

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 signicant wave height H 1/3 and a signicant wave period T s a seaway is generated, 

which is considered being matching best a natural wind sea seaway. The wave height H 1/3 is 

the average wave height (trough to crest) of the one-third largest waves, while the signicant 

wave period T s is the associated average wave period of the one-third largest waves. A typical 

Jonswap spectrum for a constant signicant wave height of H 1/3 = 7.5 m and a constant peak 

1 A spectral form for fully developed wind seas proposed by Pierson and Moskowitz (1964) 

2 A corrected Pierson Moskowitz spectrum with data from the JOint North Sea WAve Project by Hasselmann 

et al. (1973) 

10

2.2 Environmental conditions 

period of T p = 11 s is shown in gure 2.3, where the energy density spectrum S (ω) is shown 

against the wave circular frequency ω. 

Figure 2.3: Jonswap spectrum for H 1/3 = 7, 5 m and T p = 11 s 

2.2.2 Wind condition 

It is possible to consider the inuence of incoming wind on the seakeeping behavior. The governing 

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 signicant 

compared to the wind induced moments and the wind inuence can be neglected. Therefore it 

is 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 design 

and 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 are 

available. The lines of the ships for all vessels are also available. With these documents enough 

technical data are available for the calculation of the seakeeping behavior. In detail, the following 

data are entered and/or veried 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 dimensions 

like the length between perpendiculars L P P , the length over all L OA , the breadth B, the depth 

to freeboard deck D or the design draft T D . Further entered dimensions worth mentioning, are 

the keel thickness and the shell plating factor, which are needed to calculate the cross-curves of 

stability 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 accuracy. 

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 wind 

eects in the seakeeping calculations. In addition the side lateral area is very useful to assess the 

dimensions of the cuboid for the RAO calculations, as it is explained in chapter 2.1.1.1. Later 

on it is decided, not to consider the inuence of the wind on the seakeeping behavior in the rst 

step. 

13

3 Data input 

3.4 Lightship distribution 

The cuboid for determining the RAOs is calculated, based on the respective vessel's lightship 

weight and the deadweight distribution as well as their extensions. Normally a detailed lightship 

distribution in longitudinal direction is not necessary for seakeeping calculations. A coarse lightship 

weight distribution is sucient, for the same reasons which are shown in chapter 2.1.1.1. 

Anyhow, with regard to potential longitudinal strength calculations in later examinations, for 

each vessel a detailed lightship weight distribution is used for further analysis. Such calculations 

are performed to ensure sucient structural strength. The ship's structure is loaded by 

longitudinal bending moments as well as shear forces due to torsion of the hull. Therefore a detailed 

weight distribution is mandatory for longitudinal strength calculations. Picture 3.2 shows 

a 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 condition. 

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. Worth 

mentioning 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 specic center 

of gravity and the weight item's extension over the whole ship. The reasons for this coarse 

presumption 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 uid 

inuences 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 by 

the formula 3.1 shown below 

GM corrected = GM solid − ∑ i 

ρ liquid i · I tank i 

△ 

(3.1) 

for each partly lled tank i with the particular density of the liquid in tank ρ liquid , the particular 

moment of inertia of the free surface I tank and the displacement △ belonging to the particular 

loading 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 eect 

of the sloshing uid in the tank is not considered. For example this eect is used intentionally 

in roll damping tanks. 

For the seakeeping calculations it has been gured out, that both eects (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 GM solid . 

3.7 Intact stability 

The intact stability is calculated according to the intact stability code of the IMO [4]. It is 

performed to determine the limiting intact stability criterion in the examined ballast arrival 

loading condition. The following six criteria are considered: 

1. The initial metacentric height GM 0 (including free surfaces) shall not be less than 0.15 m. 

(named in the following: Initial GM is 0.15 m) 

2. The righting lever GZ shall be at least 0.2 m at an angle of heel equal to or greater than 

30 ◦ . (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 in 

the following: Max. GZ at 25 ◦ ) 

4. The area under the GZ curve shall not be less than 0.055 metre − radians up to 30 ◦ angle 

of heel. (named in the following: Area (0, 30) = 0.055 m · rad) 

5. The area under the GZ curve shall not be less than0.09 metre − radians up to 40 ◦ angle 

of heel. (named in the following: Area (0, 40) = 0.090 m · rad) 

6. The area under the GZ curve between the angles of heel of 30 ◦ and 40 ◦ shall not be less 

than 0.03 metre − radians. (named in the following: Area (30, 40) = 0.030 m · rad) 

3.8 Cross-curves of stability 

Furthermore the cross-curves of stability of the hull for xed and free trim are calculated. The 

resulting curves in E4 are compared to the curves derived from the stability booklet. The better 

the curves match, the better the E4 calculation model matches the calculating model of the 

shipyard. Thereby its assured, that the result of the calculations are applicable to the realized 

vessel. 

15

3 Data input 

At this the cross-curves for small angles should have approximately equivalent values. For large 

angles (> 60 ◦ ), the values may dier. This is due to the not considered hatchway coamings in the 

calculation models. In the scope of the subsequent analysis, this simplied model is considered 

to 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 needed 

to determine their eect on the ship's roll damping. Because the bilge keel area is not given for 

some ships, the value then has to be estimated. Therefore a mean value is calculated out of the 

given bilge keel dimensions with equation 3.2 as follows: 

mean value = 1 n 

n∑ 

i=1 

L pp i 

A BK 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, the 

bilge keel area A BK and the length between perpendicular L pp of the respective ship. According 

to the mean value, the bilge keel area for ships without given value is estimated by: 

A BK i = L pp i [ 

m 

2 ] (3.3) 

5.36 

Figure 3.3 shows the distribution of the respective bilge keel area against L pp . The numbers 

above the entries indicate the number of the examined vessel according to chapter 4. 

100,00 

90,00 

11 

Bilge keel area [m 2 ] 

80,00 

70,00 

60,00 

50,00 

40,00 

10 

estimated values 

13 

5 

6 

12 

7 

1 

3 

9 

4 

8 

2 

15 

14 

30,00 

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

L PP [m] 

Actual values of examined vessels 

Mean value curve 

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 duty 

on the vessel's bridge when the accident occurred. Hence the transversal accelerations aecting 

a human on the bridge are calculated in the further scope of this thesis. The transversal accelerations 

in seaways are calculated at one meter above the bridge deck. This value is assumed for 

the 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 why 

the transversal accelerations are inherently higher on the bridge than on lower decks. In this 

examination, the line of oatation is the ballast arrival loading condition waterline. The bridge 

height above the ballast arrival waterline of the 15 vessels against L P P is shown in gure 3.4. 


Height of bridge above ballast 

arrival waterline [m] 

42,0 

41,0 

40,0 

39,0 

38,0 

37,0 

36,0 

6 

8 

12 

35,0 

7 

34,0 

4 

33,0 

9 

32,0 13 

5 

31,0 

30,0 

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

3 

1 

Lpp [m] 


2 

14 

15 

11 

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 200 m whereas the largest vessel is more than 320 m 

long. Figure 3.5 opposes the displacement to the length between perpendicular. To visualise the 

dierences between the examined vessels, the lateral view of three of them is given. The detailed 

ship data and main dimensions for each ship are given in the respective section of chapter 4. 

130000 

120000 

110000 

14 

15 

11 

100000 

Displacement at T design [t] 

90000 

80000 

70000 

60000 

50000 

5 

6 

12 

7 

1 

3 

9 

4 

8 

2 

40000 

10 

13 

30000 

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

L PP [m] 

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 examined. 

As mentioned in chapter 2.2, the seaway is described by a signicant wave period T S and 

a signicant wave height H 1/3 . For each analysed vessel a speed v and a wave encountering angle 

is assumed according to the respective accident situation. The encountering angle is measured 

from astern, so 0 ◦ means the ship encounters a following sea. 

Table 3.1: Accident situations 

Accident Corresponds to the 

Encount. 

v [kts] 

situation accident of 

angle [ ◦ ] 

T S [s] H 1/3 [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. This 

simulation extends to 20, 000 time steps, having a step size of 0.5 s each. This corresponds to a 

total 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 simplied 

lines plan including the lateral areas and a few main dimensions. A detailed list of all 

main dimensions and the data for the respective ballast arrival loading condition can be found 

in the appendix A. In addition, some specic characteristics of the ship are named. (e.g. the 

quality of the calculation model or the hullform). At this the explanations concerning the ability 

of passing the Panama Canal, apply on the canal before its enlarging, which will be completed 

in the year 2014/2015. Further with the referenced c B value for each vessel, the neness of the 

hull 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 scenario 

the statistical distribution of the occurring accelerations is given by a histogram, where the 

maximum transversal acceleration is derived from. The mean value of the normalized amplitudes 

and the associated standard deviation as well as the number of calculated periods in the simulation 

time of 10, 000 s are also shown in the histogram. It is to be noted, that the histograms 

do not have the same scale on their x-axis. So the histograms of two dierent vessels can not be 

compared 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 

L pp 263.00 [m] 

B 40.00 [m] 

T D 12.00 [m] 

Containers 5,512 [TEU] 

The rst analysed vessel has the geometric capacity to carry 5, 512 T EU. Having the main 

dimensions according to table 4.1, this vessels must be classied as a smaller Post-Panamax 

19


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

ˆ The lines of the ship shown in gure 4.1 have a c B value of 0.57 on design draft. 

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

ˆ The stability in the ballast arrival loading condition is very high resulting in 

GM solid = 10.43 m. 

ˆ The limiting intact stability criterion (Max. GZ at 25 ◦ ) requires a GM min = 1.89 m. 

The calculated transversal accelerations on the bridge and the rolling angles for the three accident 

conditions are listed in table 4.2. 

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

Accident 

[ 

a 

situation t max m/s 

2 ] ϕ max [ ◦ ] 

Situation 1 12.5 32 



The maximum acceleration occurs for accident situation 3. With a t max = 13.5 m /s 2 for accident 

situation 3 the examination already starts with a signicant value. The statistical distribution 

of 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






L pp 292.00 [m] 

B 40.00 [m] 

T D 12.00 [m] 


The second analysed vessel has the geometric capacity to carry 6, 500 T EU. Having the main 

dimensions according to table 4.3, it belongs to the medium sized Post-Panamax vessels. The 

following characteristics of Vessel No. 02 are to be noted: 

ˆ The lines of the ship shown in gure 4.3 have a c B value of 0.61 on design draft 

ˆ The documented bilge keel area is signicantly smaller than the mean value according to 

chapter 3.9. 

ˆ The stability in the ballast arrival loading condition is very high resulting in 






Accident 

[ 

a 


2 ] ϕ max [ ◦ ] 




The maximum acceleration occurs for accident situation 3. The accelerations for Vessel 

No. 02 in situation 1 and 2 are signicant smaller than for Vessel No. 01. The statistical 

distribution of the transversal accelerations in this situation is shown in gure 4.4. 

21







L pp 263.00 [m] 

B 40.00 [m] 

T D 12.50 [m] 


The third analysed vessel has the geometric capacity to carry 5, 726 T EU. Having the main 

dimensions according to table 4.5, it belongs to the smaller Post-Panamax vessels. It has exactly 

the same main dimensions and an equivalent ballast arrival loading condition as Vessel No. 01. 

In contrast Vessel No. 03 has a higher c B value and therefore is able to carry more TEU at a 

slower design speed than Vessel No. 01. The following characteristics of Vessel No. 03 are to 

be noted: 

ˆ The lines of the ship shown in gure 4.5 have a c B value of 0.58 in design draft. 

22


ˆ The documented bilge keel area is signicantly higher than the mean value according to 

chapter 3.9. 

ˆ The stability in ballast arrival loading condition is very high resulting in a 






Accident 

[ 

a 


2 ] ϕ max [ ◦ ] 




The maximum acceleration occurs for accident situation 3, but the accelerations are comparable 

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 dierence is the 60% larger bilge keel area of 

Vessel No. 03 and therefore a higher roll damping, respectively. The accelerations in accident 

situation 2 and 3 are the same. Therefore the situation of both with the higher rolling angle is 

stated to be the worst situation. The statistical distribution of the transversal accelerations in 

this situation is shown in gure 4.6. 


23






L pp 280.75 [m] 

B 32.26 [m] 

T D 11.00 [m] 


Vessel No. 04 has the geometric capacity to carry 4, 402 T EU. Having the main dimensions 

according to table 4.7, it complies with the maximum possible main dimensions to pass through 

the Panama Canal. The vessel is the rst typical Panamax container vessel, analysed within 

this examination. The following characteristics of Vessel No. 04 are to be noted: 


ˆ The bilge keel area is not documented for this vessel and is estimated according to chapter 

3.9. 

ˆ The stability in ballast arrival loading condition is less high resulting in a GM solid = 6.39 m. 

ˆ The limiting intact stability criterion (Area (30, 40) = 0.030 m · rad) requires a 

GM min = 0.16 m. 

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 GM min in ballast arrival loading condition. The c B 

value of 0.69 is the highest value of the analysed vessels. The calculated transversal accelerations 

on the bridge and the rolling angles for the three accident conditions are listed in table 4.8. 


Accident 

[ 

a 


2 ] ϕ max [ ◦ ] 




The maximum acceleration occurs for accident situation 3. As already for Vessel No. 02, the 

occurring transversal accelerations for accident situation 1 and 2 are signicant smaller than for 

24


accident situation 3. The statistical distribution of the transversal accelerations in this situation 

is shown in gure 4.8. 






L pp 221.00 [m] 

B 32.20 [m] 

T D 11.82 [m] 


The 5th examined vessel has the geometric capacity to carry 3, 323 T EU. Having the main 

dimensions according to table 4.9, it is also able to pass the Panama Canal, but it is shorter 

than Vessel No. 04. The following characteristics of Vessel No. 05 are to be noted: 


25


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

ˆ The stability in ballast arrival loading condition is moderately high resulting in a 



GM min = 0.53 m. 




Accident 

[ 

a 


2 ] ϕ max [ ◦ ] 




For the seaways of accident situation 2 and 3, the same maximum transversal accelerations on 

the bridge occur while the accelerations in accident situation 1 are also nearly as high. Because 

the rolling angle of situation 2 is the highest, this situation is stated to be the most critical. The 

statistical distribution of the transversal accelerations in this situation is shown in gure 4.10. 


26






L pp 244.51 [m] 

B 32.25 [m] 

T D 10.00 [m] 


Vessel No. 06 has the geometric capacity to carry 4, 253 T EU . Having the main dimensions 

according to table 4.11, it is another midsized container vessel which may travel through the 

Panama Canal. The following characteristics of Vessel No. 06 are to be noted: 



3.9. 







Accident 

[ 

a 


2 ] ϕ max [ ◦ ] 




The maximum acceleration occurs for accident situation 3. The statistical distribution of the 

transversal accelerations in this situation is shown in gure 4.12. 

27







L pp 256.20 [m] 

B 32.20 [m] 

T D 10.00 [m] 


Vessel No. 07 has the geometric capacity to carry 4, 252 T EU . Having the main dimensions 

according to table 4.13, the vessel is also a midsized, Panama canal capable container ship 

very similar to Vessel No. 06. The following characteristics of Vessel No. 07 are to be noted: 


ˆ The documented bilge keel area is slightly smaller than the mean value according to chapter 

3.9. 

28





Compared to Vessel No. 06, the c B value of Vessel No. 07 is slightly larger and the GM min 

is slightly smaller. The calculated transversal accelerations on the bridge and the rolling angles 

for the three accident conditions are listed in table 4.14. 


Accident 

[ 

a 


2 ] ϕ max [ ◦ ] 




As for Vessel No. 06 the maximum acceleration occurs for accident situation 3. The accelerations 

in situation 1 and 2 are also in the same scope for both vessels. Furthermore the dierences 

between 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 accelerations 

in this situation is shown in gure 4.14. 


29






L pp 283.20 [m] 

B 32.20 [m] 

T D 11.00 [m] 



according to table 4.15, it is a typical Panamax container vessel like Vessel No. 04. The 

following characteristics of Vessel No. 08 are to be noted: 


ˆ The documented bilge keel area is slightly larger than the mean value according to chapter 

3.9. 



GM min = 0.40 m. 

As for Vessel No. 04, the rst analysed Panamax vessel, the c B value is relatively high for a 

container vessel and the GM min is small. The calculated transversal accelerations on the bridge 

and the rolling angles for the three accident conditions are listed in table 4.16. 


Accident 

[ 

a 


2 ] ϕ max [ ◦ ] 




The maximum acceleration occurs for accident situation 3. The distribution of the highest 

accelerations 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 for 

situation 2. The statistical distribution of the transversal accelerations in this situation is shown 

in gure 4.16. 

30







L pp 277.00 [m] 

B 32.25 [m] 

T D 12.20 [m] 



according to table 4.17, it is a typical Panamax container vessel like Vessel No. 04 and Vessel 

No. 08. Due to its design draft of 12.2 m, the vessel is not able to pass the Panama Canal in 

design loading condition, because in the canal the draft is limited to 12.04 m. Another loading 

condition with a smaller draft has to be chosen for the passage. The following characteristics of 

Vessel No. 09 are to be noted: 

ˆ The lines of the ship shown in gure 4.17 have a c B value of 0.65 on design draft. Furthermore 

the slanted transom is unusual. 

31


ˆ The documented bilge keel area is slightly smaller than the mean value according to chapter 

3.9. 

ˆ The stability in ballast arrival loading condition is less high resulting in the smallest GM 

of the examination GM solid = 5.09 m. 


GM min = 0.32 m. 

Like the other Panamax vessels, also Vessel No. 09 has a relatively high c B value and a very 

small GM min . The calculated transversal accelerations on the bridge and the rolling angles for 

the three accident conditions are listed in table 4.18. 


Accident 

[ 

a 


2 ] ϕ max [ ◦ ] 




Until now the maximum transversal acceleration of 14 m /s 2 in situation 3 is the worst value 

calculated. As for Vessel No. 04 and Vessel No. 08, the highest acceleration value occurs for 

situation 3, while the lowest is associated to situation 2. Notable is the fact, that the highest 

value is twice as high as the lowest. The statistical distribution of the transversal accelerations 

in this situation is shown in gure 4.18. 


32






L pp 195.40 [m] 

B 29.80 [m] 

T D 10.10 [m] 



according to table 4.19, it is the smallest analysed vessel. In addition it is the only vessel equipped 

with cranes and a deck house located at the ship's aft end. The following characteristics of 

Vessel No. 10 are to be noted: 



3.9. 



GM min = 0.38 m. 




Accident 

[ 

a 


2 ] ϕ max [ ◦ ] 




The maximum acceleration of 14.5 m /s 2 occurs for accident situation 2 while the associated 

rolling angle of 43 ◦ is the highest calculated value in the whole examination. The statistical 

distribution of the transversal accelerations in this situation is shown in gure 4.20. 

33







L pp 322.60 [m] 

B 45.60 [m] 

T D 13.00 [m] 



according 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: 


ˆ The documented bilge keel area is much larger than the mean value according to chapter 

3.9. 

ˆ The stability in ballast arrival loading condition is extremely high resulting in a 


34



The ship is very ne with its c B value of 0.59. The stability values GM solid and mainly GM min 

have a signicant higher order of magnitude, than the values of the previous analysed vessels. 




Accident 

[ 

a 


2 ] ϕ max [ ◦ ] 




The maximum acceleration occurs for accident situation 3. But the calculated accelerations are 

considerably smaller than for the previous analysed vessels. The statistical distribution 

of the transversal accelerations in this situation is shown in gure 4.22. 


35






L pp 249.03 [m] 

B 32.20 [m] 

T D 11.30 [m] 



according to table 4.23, it is another midsized container vessel which may travel through the 

Panama Canal. The vessel is comparable to Vessel No. 07, which has nearly the same 

dimensions, a slightly smaller c B value and therefore a ner hullform as well as a smaller geometric 

TEU capacity. The following characteristics of Vessel No. 12 are to be noted: 


ˆ The documented bilge keel area is signicant smaller than the mean value according to 

chapter 3.9. 







Accident 

[ 

a 


2 ] ϕ max [ ◦ ] 




The maximum acceleration occurs for accident situation 3. The maximum acceleration is 

higher, than for the comparable Vessel No. 07. The statistical distribution of the transversal 

accelerations in this situation is shown in gure 4.24. 

36







L pp 210.25 [m] 

B 30.00 [m] 

T D 10.10 [m] 



according to table 4.25, it is the second smallest analysed vessel. The following characteristics 

of Vessel No. 13 are to be noted: 


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



37



GM min = 0.65 m. 




Accident 

[ 

a 


2 ] ϕ max [ ◦ ] 




The maximum acceleration occurs for accident situation 2. The transversal acceleration of 

15 m /s 2 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 accident 

situation 2, while for the other vessels the critical situation is situation 3. Apparently the seaway 

in situation 2 with a shorter signicant wave period of T S = 8.5 s stronger excites the small 

vessels. The statistical distribution of the transversal accelerations in this situation is shown in 

gure 4.26. 


38






L pp 319.00 [m] 

B 42.80 [m] 

T D 13.00 [m] 



according to table 4.27, it belongs to the class of the large Post-Panamax vessels. With Vessel 

No. 14 the Chicago Express takes part of the analysis, which is the vessel involved in accident 

situation 1. For the BSU accident report [1] it has already been examined, although referring to 

a dierent loading condition. The following characteristics of the Chicago Express are to be 

noted: 


ˆ The documented bilge keel area is a little bit larger than the mean value according to 

chapter 3.9. 




Besides Vessel No. 11, the Chicago Express is the second vessel in the examination out 

of the class of large Post-Panamax vessels. With a c B value of 0.66, the Chicago Express 

has not such a ne shaped hull as Vessel No. 11. But the stability values GM solid and most 

notably GM min also have a signicant higher order of magnitude, than the values for the smaller 

analysed vessels. The calculated transversal accelerations on the bridge and the rolling angles 

for the three accident conditions are listed in table 4.28. 


Accident 

[ 

a 


2 ] ϕ max [ ◦ ] 




39


The maximum acceleration occurs for accident situation 2. As for the rst large vessel analyse, 

Vessel No. 11, the calculated accelerations are considerably smaller than for the previous 

analysed 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






L pp 319.00 [m] 

B 42.80 [m] 

T D 13.00 [m] 


The last analysed vessel has the geometric capacity to carry 8, 200 T EU. Having the main 

dimensions according to table 4.29, it belongs to the large Post-Panamax vessels. The vessel is 

very similar to the Chicago Express as it has exactly the same main dimensions as well as an 

equivalent ballast arrival loading condition. The following characteristics of Vessel No. 15 are 

to be noted: 

ˆ The lines of the ship shown in gure 4.29 have a c B value of 0.65 on design draft 

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

ˆ The calculated cross-curves in E4 coincide well with the ones stated in the trim & stability 

booklet 


GM solid = 12.49 m 

ˆ The limiting intact stability criterion (Max. GZ at 25 ◦ ) requires a GM min = 4.77 m 




Accident 

[ 

a 


2 ] ϕ max [ ◦ ] 




The maximum acceleration occurs for accident situation 3. Although Vessel No. 15 is very 

similar to the Chicago Express, the accelerations dier. The statistical distribution of the 

transversal accelerations in this situation is shown in gure 4.30. 

41



42

5 Evaluation 

Based on the determination of the seakeeping behavior in the previous chapter, the following 

sections summarize and explain the results, highlight the consequences and give recommendations 

for 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 of 

hull form and ship design. This is due to the necessity to carry as much containers as possible 

on 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 c B values in a scope of 0.57 ... 0.69. 

The results show, that the transversal accelerations on the bridges are correlated with the 

respective rolling angles. Therewith it is not implied, that one explicit rolling angle always 

causes one explicit acceleration. But it can be stated, that high accelerations only occur in 

combination with large rolling angles. 

Summing up the results of the examination of the single ships in the ballast arrival loading 

condition reveals: 

ˆ In their ballast arrival loading condition all examined ships have, more or less, a GM value, 

which is signicantly higher than the required minimum GM min according to the rules of 

the IMO[4]. It can be stated, that all vessels considered have a very high stability. 

ˆ Most vessels experience large rolling angles up to 40 ◦ and high transversal accelerations on 

the bridge up to 15 m /s 2 , depending on the examined accident situation named in chapter 

3.12. 

To get an overview of the examination, all calculated transversal acceleration on the bridge 

against their respective GM solid are plotted in gure 5.1. The numbers in gure 5.1 represent 

the respective vessels in chapter 4. At this, the maximum transversal acceleration is plotted for 

each of the three accident situations. For better comparison of the occurring accelerations, two 

of 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 the 

graph for each of the three analysed accident situations. 

43

5 Evaluation 

Transverse acceleration on the bridge in 

ballast arrival loading condition [m/s 2 ] 

16 

14 

12 

10 

8 

6 

4 

2 

0 

9 

2468 TEU in 

accident 

10 

8 

4 

13 12 

5 

7 

6 

CE in accident 

2 

3 

1 

15 

14 = CE 

4 6 8 10 12 14 

GM solid [m] 

11 

Accident situation 1 Accident situation 2 Accident situation 3 

Figure 5.1: Transversal accelerations on the bridge against GM solid 

5.2 Consequences 

Normally it is expected that large vessels with a length of over 200 m or even 300 m are relatively 

safe in heavy sea and do not experience an exceptional seakeeping behavior. But the analysis 

reveals, that most of the considered container vessels apparently have signicant problems with 

their seakeeping behavior in combinations of certain loading and environmental conditions. 

In exception to the above stated the three largest vessels, namely Vessel No. 11, Vessel 

No. 14 and Vessel No. 15, experience smaller rolling angles and accelerations during the examination 

(see gure 5.1). Simply looking at this result, it could be concluded, that these large 

vessels 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 described 

with accident situation 1 (refer to table 3.1). During this accident very high rolling angles 

and transversal accelerations on the bridge occurred in a dierent loading condition (compare 

BSU report [1]). 

The examined ballast arrival condition diers from the accident loading condition. The 

Chicago Express now has a smaller displacement and GM as well as a dierent trim. This 

implies that the other large vessels, Vessel No. 11 and Vessel No. 15 may also be endangered 

to experience equally high high transversal accelerations in a dierent loading condition. This 

assumption is analysed further in chapter 6.2. 

The problems in the seakeeping behavior occur due to the following reasons: The shaped hull 

form and the signicant bow are of the analysed vessels favours the impact of direct, exciting 

heeling moments through the heavy sea. On the other hand, the excessive stability causes high 

restoring moments of the heeled vessel. This results in signicant 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 a 

wide scope of examined GM solid 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 value 

for the maximum transversal accelerations acting on humans on the bridge does not exist. For 

example according to the DNV rules [12], the transversal dynamic acceleration taking eect on 

container lashings on deck, shall be taken not smaller than ∼ 0, 5 g. The calculated accelerations 

on the bridge partly exceed the triple of that value. In the same time the normalized mean value 

of the occurring acceleration amplitudes mostly exceeds a value of ∼ 0, 5 g (refer to the respective 

histograms in chapter 4). Such high transversal accelerations are considered being denitely not 

acceptable. 

5.3 Recommendations 

The simulation results show, that the ballast arrival loading condition of container vessels is 

not a safe seagoing condition. The risk of encountering excessive rolling angles and very high 

transversal accelerations on the bridge in heavy sea is increased signicantly. Based on the 

simulation results, the following approaches to reduce the risk of accidents can be exemplied. 

5.3.1 Stability 

Concerning the stability of the vessels, no universally valid GM value, which reduces the risk of 

accidents, can be derived from the analysis. The seakeeping behavior of a ship apparently has 

a lot of important additional inuence factors. For instance two of the factors which have to 

be considered, are the ship's trim and the hull form. Altogether the factors can form a critical 

ship 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 to 

be done with adequate methods for each vessel individually. A general prediction of a critical 

situations 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 motions 

and transversal accelerations on the bridge. There are dierent ways to increase the roll damping 

of a ship. According to Abdel-Maksoud [11] the following possibilities t for this purpose: 

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

ˆ Increase the ship's speed at low speeds → roll damping by shear stress on the hull, angular 

incoming ow on the rudder and immersed transom 

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

For a vessel already in service, the bilge keels could be modied easily. Though such a modication 

would not have a deciding inuence on the transversal accelerations. In appendix B.1 a 

graph can be found, where the bilge keel area is changed for Vessel No. 13, being the vessel 

with the highest occurring transversal acceleration value during the examination. In the graph 

the 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 transversal 

accelerations of about 10 %. A general advantage of bilge keel is, that they also function with 

zero speed. 

45

5 Evaluation 

Furthermore the increase of the ship's speed always reduces the roll motion. But at rst the 

vessel has to be able to signicantly increase the speed, which is not self-evident due to the high 

wave forces slowing the ship with each wave. On the other hand a higher ship's speed in heavy 

seaway causes high slamming loads on the ship's bow structure, when heading into the waves. 

This eect 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 of 

encountering a critical 2:1 resonance. Therefore the augmentation of the ship's speed to improve 

the roll damping is suitable to only a limited number of cases. The inuence of ship's speed is 

also determined for Vessel No. 13. The associated graph in appendix C.1 shows that the ship's 

speed has not a signicant inuence, too. For this analysis, the vessel in ballast arrival condition 

encounters 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 and 

reduces 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 inuence on the seakeeping behavior. As mentioned 

before, the shape of the frames or rather the shape of the bow are in combination with 

the wide transom, governs the induced rolling moments. Already during the very early design 

phase, the following compromise has to be determined. On one hand the vessel is intended to 

carry as much cargo as possible which results in aring hull forms. On the other hand this often 

contradicts with the demand of a good seakeeping behavior. 

5.3.4 Other 

The operating behavior of the crew has also an inuence. 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 at 

zero speed. In beam sea a lot of the wave energy induced into the ship is transformed into a 

drift motion in beam direction. Therefore the roll motions of the vessel are reduced. A problem 

in this position can be, that the ship's stern turns into the waves due to the poor course keeping 

ability 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 obviously 

not advisable inshore. 

46

6 Detailed examination 

The evaluation discussed in chapter 5 discloses, that further investigations are necessary for the 

better understanding of the high transversal acceleration problem. For this reason the following 

detailed examinations are carried out. 

At rst, the inuence of the ship's stability on the transversal accelerations is analysed. Furthermore 

it has to be examine, if the large vessels, Vessel No. 11 and Vessel No. 15, are also 

endangered to encounter high acceleration and rolling angle values in a loading condition similar 

to the one of Vessel No. 14 (Chicago Express) when it experienced severe ship motions in 

accident. 

6.1 Variation of the GM values 

In this chapter the inuence of the initial stability (namely GM) on the occurring transversal 

acceleration for three out of the 15 examined vessels is determined. In order to consider the 

probable inuence 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 GM solid is varied by changing the 

vertical center of gravity KG of the vessel. The calculations are performed without considering 

the inuence of free surfaces, for the reasons named in chapter 3.6. The displacement as well as 

the ship's trim of the analysed ballast arrival condition are kept constant. For each GM value 

all three accident situations according to chapter 3.12 are simulated. 

In addition it is estimated, if such a GM solid 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 inner 

bottom is not realistic. The feasible minimum KG depends on the light ship's vertical center of 

gravity, the position and lling of the ballast water and fuel oil tanks in the lower part of the 

ship as well as cargo in the holds. 

A shifted GM directly aects the seakeeping behavior. Hence to represent well the dierences, 

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

GM value. 

6.1.1 Small vessel 

Vessel No. 13 was chosen as smallest vessel for the detailed stability analysis. Its relevant data 

are listed in table 6.1. More main dimension data of this vessel can be found in the appendix A.13 

on page 71. The GM is varied around the ballast arrival GM solid = 6.98 m within a range of 

about GM ∼ = 3 ... 12 m. 

In gure 6.1 the resulting transversal accelerations on the bridge are shown related to the 

dierent GM solid values. All three accident situations result in a comparable curve slope. In 

accident situation 1 and 2 the highest accelerations occur for the GM value of the ballast arrival 

loading condition. In accident situation 3 the highest acceleration occurs for a higher GM of 

about 8 m. With a higher or a lower stability the vessel would experience signicantly smaller 

accelerations. Though just a GM solid value of 8 ... 9 m is realistically reachable for this vessel by 

e.g. lling ballast water in tanks in low positions. Higher values in this simulation can only be 

reached by decreasing the vertical center of gravity of the lightship weight, which is considered 

being impossible for an existing vessel. 

47


Table 6.1: Stability data for the small vessel 

Ballast arrival loading 

Value Unit 

condition 

KM 15.46 [m] 

KG 8.48 [m] 

GM solid 6.98 [m] 

Light ship Value Unit 

vcg LSW 12.18 [m] 

16 

14 

Maximum transverse acceleration on the bridge [m/s 2 ] 

12 

10 

8 

6 

4 

2 

Ballast arrival loading condition 

0 

2 4 6 8 10 12 14 16 

GM solid [m] 


Figure 6.1: Vessel No. 13 in ballast arrival oating condition: Variation of GM solid 

6.1.2 Midsized vessel 

The midsized vessel for the detailed stability analysis is Vessel No. 1. Its relevant data are listed 

in table 6.2. More main data of this vessel can be found in the appendix A.1 on page 59. The GM 

is varied around the ballast arrival GM solid = 10.43 m within a range of about GM ∼ = 5 ... 13 m. 


varied GM solid values. All three accident situations result in a comparable curve slope. On 

average the highest accelerations occur for a GM in the range of the GM solid within the ballast 

arrival loading condition. It is very mentionable, that the vessel would also experience lower 

transversal accelerations on the bridge, even when the stability is further increased. Though just 

a GM solid value of about 11 m is realistically reachable for this vessel by e.g. lling tanks in 

low positions. Again, higher GM values are only realisable by changing the vertical center of 

gravity of the lightship weight. When reducing the stability by decreasing GM, the transversal 

48

6.1 Variation of the GM values 

accelerations also decrease signicantly to values of about 3 m /s 2 . 

Table 6.2: Stability data for the midsized vessel 


Value Unit 

condition 

KM 21.45 [m] 

KG 11.02 [m] 



vcg LSW 15.13 [m] 

16 

14 


12 

10 

8 

6 

4 

2 


0 

2 4 6 8 10 12 14 16 

GM solid [m] 


Figure 6.2: Vessel No. 01 in ballast arrival oating condition: Variation of GM solid 

6.1.3 Large vessel 

The large vessel for the detailed stability analysis is the Chicago Express. Its relevant data 

are 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 GM solid = 12.40 m in both directions within a range 

of about GM ∼ = 5 ... 15 m. 


varied GM solid values. For all three accident situations it follows a comparable curve slope. This 

time no signicant transversal accelerations occur in the ballast arrival loading condition. With 

a higher stability, than in the ballast arrival loading condition, the behavior of the vessel does 

not change. Furthermore all analysed GM solid values up to 14 m are realistically reachable for 

49


this vessel by e.g. lling ballast water in tanks in low positions. When reducing the GM of the 

ballast arrival loading condition, the transversal accelerations increase signicantly up to 10 m /s 2 

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

Mentionable is the fact, that the accident of the Chicago Express occurred in a loading 

condition with the same GM = 8.54 m. (refer to BSU report [1]). 

Table 6.3: Stability data for the large vessel 


Value Unit 

condition 

KM 25.64 [m] 

KG 13.24 [m] 



vcg LSW 15.62 [m] 

16 

14 


12 

10 

8 

6 

4 

2 


0 

2 4 6 8 10 12 14 16 

GM solid [m] 


Figure 6.3: Chicago Express in ballast arrival oating condition: Variation of GM solid 

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 the 

other accident situations, the curve shape is comparable. It can be identied, that each vessel has 

a 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 

16 

14 


12 

10 

8 

6 

4 

2 

0 

2 4 6 8 10 12 14 16 

GM solid [m] 

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

Figure 6.4: Comparison of the stability inuence 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 experience 

high rolling angles nor high transversal accelerations on their bridges. But the Chicago Express 

is denitely endangered to experience very high transversal accelerations, as e.g. when 

it encountered accident situation 1 and high transversal accelerations of up to 10 m /s 2 occurred 

(refer to BSU report [1]). The data of the loading condition during the accident is shown in 

table 6.4. Therefore it is presumed, that the other two large vessels also reach high transversal 

accelerations, when they operate in such a loading condition. This presumption shall examined 

in the following. 

For this reason the seakeeping behavior of the two other large vessels is determined for several of 

such comparable loading conditions. To achieve more clarity, the results of this investigation are 

only shown for accident situation 1, being the Chicago Express accident situation. (compare 

section 3.12) 

51


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

Main 

Value Unit 

dimensions 

△ 66649 [t] 

T AP 9.07 [m] 

T F P 7.08 [m] 

T rim -1.99 [m] 

KM 23.36 [m] 

KG 14.82 [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 and 

therefore the GM solid are varied in the scope of the GM solid CE of the Chicago Express during 

the accident, while the displacement, the drafts and the trim are kept constant. These values 

comply 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 

Value Unit 

dimensions 

△ 66649 [t] 

T AP 9.19 [m] 

T F P 7.20 [m] 

T rim -1.99 [m] 

KM 23.19 [m] 

KG variable [m] 

GM solid variable [m] 

Table 6.6 species the resulting transversal accelerations on the bridge and the respective 

GM solid values in accident situation 1. The GM solid is randomly varied in the analysed scope. 

The associated curve is shown in gure 6.5. For comparison, the transversal acceleration according 

to the GM solid CE for the Chicago Express in its accident loading condition is included in 

the gure. 

The results prove the initial hypothesis to be correct. Vessel No. 15 is also endangered to 

suer high transversal acceleration on its bridge in a slightly dierent loading condition, than 

the ballast arrival loading condition. 

52


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

Loading GM solid [m/s 

a t max 

conditions [m] 

2 ] 

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 

12 


10 

8 

6 

4 

2 

0 

5 6 7 8 9 10 11 12 

GM solid [m] 

Vessel No.15 in CE accident condition 

CE in accident 

Figure 6.5: Vessel No. 15: Variation of GM solid 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 in 

appendix A.11. The oating condition shown in table 6.7 is set for Vessel No. 11. The KG 

and therefore the GM solid are again randomly varied in the range of GM solid CE of the Chicago 

Express during the accident. The displacement, drafts and trim in this oating condition are 

kept 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 condition 

and a varied GM solid value, is then used to determine the respective seakeeping behavior. 

53


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

Main 

Value Unit 

dimensions 

△ 66649 [t] 

T AP 9.07 [m] 

T F P 7.08 [m] 

T rim -1.99 [m] 

KM 24.30 [m] 



The results listed in table 6.8 show, that Vessel No. 11 at rst does not experience excessive 

transversal accelerations . However for GM solid = 9.28 m a slightly maximum for the transversal 

acceleration of 5.5 m /s 2 is already considered to be noticeable. So for this specic sea condition 

within accident situation 1, a GM solid value of about 9 m leads to the highest, but insignicant 

accelerations. 

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

Loading GM solid [m/s 

a t max 

conditions [m] 

2 ] 


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 be 

determined, where the constant excitation of the seaway results in high accelerations. For this 

reason the vessel is immersed slightly deeper. The new oating condition shown in table 6.9 is 

set. A new compilation of loading conditions is then created by varying GM in the same scope 

as before. 

Table 6.9: Vessel No. 11: New oating condition 

Main 

dimensions 

Value Unit 

△ 80,000 [t] 

T AP 10.68 [m] 

T F P 8.69 [m] 

T rim -1.99 [m] 

KM 23.53 [m] 



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

54


riences signicant higher transversal accelerations on the bridge up to 10 m /s 2 , than within the 

loading condition summarized in table 6.7. As in the CE alike loading condition, the maximum 

value occurs for a GM solid of about 9 m. The associated curves for both loading conditions are 

shown in gure 6.6. For comparison, the situation of the Chicago Express in its accident 

loading 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 transversal 

accelerations on its bridge. Therefore all vessels, including the large vessels have an increased 

risk of accident in the examined seaways. 

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

GM 

Loading condition solid [m/s 

a t max 

[m] 

2 ] 


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 

12 

Maximum transverse acceleration on the bridge [m/s2] 

10 

8 

6 

4 

2 

0 

5 6 7 8 9 10 11 12 

GM solid [m] 

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

Figure 6.6: Vessel No. 11: Variation of GM solid in dierent loading conditions 

In addition, the curves in gure 6.6 conrm the statement, already given in chapter 5.2. This 

examination clearly shows, that the problem of high accelerations on the bridge is denitely not 

a pure stability problem. Here the dierences 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 1.6 m 

for the second loading condition set. For a vessel of this size, these dierences do not seem 

remarkable. Nevertheless for one of the rst loading conditions, a moderate maximum transversal 

acceleration of 5.5 m /s 2 occurs, while for one of the second loading conditions, the value becomes 

signicantly higher, reaching an extremum of 10 m /s 2 . These maximum accelerations occur for a 

GM solid 

∼ = 9.25 m in both cases. 

The analysis reveals that signicantly dierent accelerations may occur for similar GM values 

and just slightly dierent 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 excessive 

stability 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 vessels 

have a signicant 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 have 

no or only few cargo on board resulting in rather small drafts and thus high stability values. For 

twelve of the analysed vessels the ballast arrival loading condition is most critical while for the 

three 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 inuence on the 

seakeeping behavior. Therefore a simple approach like the determination of a single upper limit 

for the GM does not seem to be a feasible approach to avoid such accidents in the future. 

Particularly due to distinctive nonlinear eects, mainly on the roll motion, the seakeeping 

behavior can denitely not be calculated with simple linear approaches. Therefore it is recommended, 

that the seakeeping behavior for each single loading condition should be evaluated 

during the early design process by the application of numerical methods, which are capable to 

simulate these nonlinearities. In this way it can be identied, whether a ship's ballast arrival 

loading condition should be stated to be a seagoing condition or if there is an increased risk 

of accident. With such methods, it is possible to reproduce the behavior of the ships during 

real accidents very well (refer to the accident reports [1][2][3]). Thus the seakeeping calculations 

performed for this thesis, also represent well the real seakeeping behavior of the analysed vessels 

and are adequate to estimate the risk of encountering an accident. 

Having gained this knowledge, it becomes obvious that there is a need for establishing mandatory 

regulations for the determination of the seakeeping behavior and to increase the safety on 

the bridges for the crew. 

Furthermore, since the excessive stability alone is not responsible for the accidents, the operating 

could be considered as main cause. This is not reasonable, because the crew of all vessels 

within the analysed accident situations [1][2][3] followed a good seamanship for the behaviour 

in 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 is 

ensured, that vessels keep their manoeuvrability and do not face high slamming loads on the 

bow structure as well as green water on deck. These eects can cause severe damages on the 

ship'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 recommended 

to perform reliable calculations during the ship design and the approval process in order to 

identify 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 L oa 274.60 [m] 

Length between perpendiculars L pp 263.00 [m] 

Breadth B 40.00 [m] 

Depth to freeboard deck D 24.20 [m] 

Design draft T D 12.00 [m] 

Full scantling draft T F S 14.00 [m] 

Lightship weight LSW 23110 [t] 

Displacement at T D △ design 73792 [t] 

Block coecient at T D c B 0.57 - 

Service speed v S 26.6 [kts] 

Number of containers - 5512 [T 

[ 

EU] 

Maximum ballast water capacity - 14349 m 

3 ] 

[ 

Total bilge keel area A BK 42.50 m 

2 ] 

Height of the bridge above baseline - 46.50 [m] 

Ballast arrival condition data Symbol Value Unit 

◦ 

Ballast arrival displacement △ BallArr 37276 [t] 

[ 

Used water ballast capacity - 12077 m 

3 ] 

Draft at after perpendicular T AP 9.05 [m] 

Draft at forward perpendicular T F P 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. GM solid 10.43 [m] 

Minimum metacentric height GM req. 1.89 [m] 

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

59

A Vessel data 















[ 

EU] 


3 ] 

[ 


2 ] 




[ 


3 ] 








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

60
















[ 

EU] 


3 ] 

[ 


2 ] 



◦ 


[ 


3 ] 









61

A Vessel data 















[ 

EU] 


3 ] 

[ 


2 ] 




[ 


3 ] 








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

62
















[ 

EU] 


3 ] 

[ 


2 ] 




[ 


3 ] 









63

A Vessel data 















[ 

EU] 


3 ] 

[ 


2 ] 




[ 


3 ] 









64
















[ 

EU] 


3 ] 

[ 


2 ] 



GZ ◦ 


[ 


3 ] 








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

65

A Vessel data 















[ 

EU] 


3 ] 

[ 


2 ] 




[ 


3 ] 









66
















[ 

EU] 


3 ] 

[ 


2 ] 




[ 


3 ] 









67

A Vessel data 















[ 

EU] 


3 ] 

[ 


2 ] 




[ 


3 ] 









68
















[ 

EU] 


3 ] 

[ 


2 ] 



◦ 


[ 


3 ] 









69

A Vessel data 















[ 

EU] 


3 ] 

[ 


2 ] 




[ 


3 ] 









70
















[ 

EU] 


3 ] 

[ 


2 ] 




[ 


3 ] 









71

A Vessel data 















[ 

EU] 


3 ] 

[ 


2 ] 




[ 


3 ] 









72
















[ 

EU] 


3 ] 

[ 


2 ] 



◦ 


[ 


3 ] 









73

A Vessel data 

74

B Variation of the bilge keel area 

18 

16 


14 

12 

10 

8 

6 

4 

2 

0 

20 25 30 35 40 45 50 55 60 65 70 

Bilge keel area [m 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 

16 

14 


12 

10 

8 

6 

4 

2 

0 

0 2 4 6 8 10 12 

Ship's speed [kts] 

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; Sea 

conditions of accident situation 2 

77

C Variation of the ship's speed 

78

Bibliography 

[1] BSU; Federal Bureau of Maritime Casualty Investigation (2009): Untersuchungsbericht 

510/08 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 Schies E.L.M.A. Tres durch Seegang 

am Vormittag des 26.11.1981; Schrift Nr. 2327 Institut für Schibau Universität Hamburg 

[6] Kröger, P. (1987): Simulation der Rollbewegung von Schien im Seegang; Bericht Nr. 

473 Institut für Schibau Universität Hamburg 

[7] Krüger, S. and others (2010): Stability Accidents in Ballast/Laid-Up Conditions - A new 

phenomenon?; Conference paper for PRADS conference 2010 

[8] Kluwe, F. (2009): Development of a Minimum Stability Criterion to Prevent Large Amplitude 

Roll Motions in Following Seas; Bericht Nr. 648 Schriftenreihe Schibau; ISBN 

978-3-89220-648-4 

[9] Blume, P. (1979): Experimentelle Bestimmung von Koezienten der wirksamen Rolldämpfung 

und ihre Anwendung zur Abschätzung extremer Rollwinkel; Schistechnik Band 26 

[10] GRIM, O. (1961): Beitrag zu dem Problem der Sicherheit des Schies im Seegang; 316. 

Mitteilung der Hamburgischen Schibau-Versuchsanstalt; Schi und Hafen 1961 Heft 6 

[11] Abdel-Maksoud, M. (2010): Skriptum zur Vorlesung Seeverhalten von Schien; Technische 

Universität Hamburg-Harburg 

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

G300 

79

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