On the dynamic stability problems of Ro-Ro ships

VETENSKAP OCH KONST

tsT,CW)-KTH

Stockholm

1995

On the Dynamic Stability

Problems of RoRo-Ships

Doctoral Thesis

Jianbo Hua

TECHNISCHE UNIVERS!' FLIT

Scheepshydromechanica

itrchief

Mekelweg 2, 2628 CD Delft Te1:015-2786873/Fax:2781836

NAVAL ARCHITECTURE

DEPARTMENT OF VEHICLE ENGINEERING ROYAL INSTITUTE OF TECHNOLOGY

Laboratorium voor

KuNGL _{Scheepshydromechanica}

TEKNISKA _Archie

HOGSKOLAN _{MakeIweg 2,2628 CD Delft}

Tal: 015- 788873 - Fax: 015- 78133B

Naval Architecture

Department of Vehicle Engineering December 1995

On the Dynamic Stability Problems

of RoRo-Ships

by

Jianbo Hua

ISSN 1103-470X

ISRN KTH/FKT/SKP/FR--95/49--SE

Address: Visiting address:

Naval Architecture °sears backe 33

Dept of Vehicle Engineering Royal Institute of Technology, KTH S-100 44 Stockholm, Sweden

Telphone: Telefax: Seer: +46 8 790 75 21 +48 8 790 6684 Switch: +46 8 790 60 00

This doctoral thesis deals with dynamic stability problems of RoRo-ships, covering three aspects:

analysis of capsize incidents of some RoRo-ships, development of analysis tools,

and studies of some dynamic stability problems of RoRo-ships.

Three capsize incidents of the RoRo-ships "Herald of Free Enterprise", "Vinka Gorthon" and "Zenobia" have been analysed by means of theories of ship dynamics in calm water and in waves.

Development of analysis methods progressed continuously during the period

1986-1994 in connection with the author's research activity in analysing

practical dynamic problems and resulted in SMS - a platform in terms of

computer code for ship dynamic analysis in time-domain.

Some research works have been carried out in order to investigate

parametrically excited roll motion and the simultaneous effect of wave-induced ship motions on cargo shifting. A derivation has been made so that the GM-variation of a ship in waves can be represented as a Volterra system. Thereby the explicit relationship between the hull form and its GM-variation in waves

can be obtained.

Key words

dynamic stability problems, RoRo ships, capsize accident, capsize analysis, time-domain simulation, code development, theoretical study, manoeuvre

motion, ship motions in waves, parametrically excited

roll motion,

This dissertation is based on the following six appended papers: Paper A.

Paper B.

Hua, J. 1988 "A Theoretical Study on the Capsize of the Ferry HERALD OF FREE ENTERPRISE", The Royal Institute of

Technology, Department of Naval Architecture, 1988, TRITA-SKP 1062. Recently accepted by"International Shipbuilding Progress

for publication

Hue, J. 1992 "A Study of the Parametrically Excited Roll Motion of

a RoRo-Ship in Following and Heading Waves ",

International Shipbuilding Progress, 39, no.420 (1992) pp.345-366

Paper C. Hua J. and Palmquist M., 1994, "A Description of SMS - A computer code for ship motion simulation", TRITA-FKT Report

9520, ISSN 1103-470X, ISRN KTH/FKT/SKP/F'R-95102-SE,

The Royal Institute of Technology, Division of Naval Architecture, 1994

Paper D. Hua, J. and Rutgersson, 0, 1994 " A Study of the Dynamic

Statbility of a RoRo-Ship in Waves ", STAB'94, Florida, Nov. 1994

Paper E. Hua, J., 1994 " A Representation of a Ship's GM-variation in

Waves by the Volterra System", Oct. 1994. Unpublished.

Paper F Hua, J., 1994 "A Probabilistic Study of the Simultaneous Effect of Ship Motions on the Cargo Onboard",

be scheduled for publication in January 1996 issue of Marine Technology

After one and a half years of study in the field of ship and offshore structures, which resulted in a technical licentiate degree at the beginning of 1986, my research work began moving towards ship dynamics, with support from Prof.

Erik Steneroth. The involvement in investigations of several capsizing

incidents, e.g. the RoRo/passenger-ship"Herald of Free Enterprise", forms the basis for this work.

This thesis consists of six selected papers written during the years 1986 - 1995. Actually, I've not had any priority during this period to write a doctoral thesis

until Autumn 1994. So these papers together are not well structured as a

regular thesis. Therefore, in the introduction, see pp. 1-26, I try to make a systematic summary of both the works described in those six papers and in my

other papers, and present the accumulated knowledge in order to give a

general view of my work.

The thesis covers the following three aspects; analysis of some capsizing incidents,

tool development in form of computer code for analysis of ship

dynamics,

study of some dynamic stability problems of RoRo-ships.

In fact, these three aspects reflect the main character of my research activity

at the Royal Institute of Technology, Sweden.

It should be acknowledged that my research work during the years 1986-1995

have been financially supported mainly by the Swedish Shipbuilders

Association and the National Swedish Board for Technical Development, and later by the National Program for Ship Research in Sweden. The financial support was also achieved for some projects from Gists. Lundeqvists fond at the

Royal Institute of Technology.

With great support and successful co-operation from my colleagues Mikael Huss and Mikael Palmquist, to whom I am grateful. Finally I would like to express my thanks to Professor 011e Rutgersson for his kindness in providing

1 Introduction 1

2 Analysis of some capsize incidents 3

2.1 Capsizing of "Herald of Free Enterprise" 4

2.2 Capsizing of the RoRo-ship " Vinka Gorthon " 6

2.3 Capsize of "Zenobia" 9

3 Development of analysis tool 11

3.1 Ship manoeuvre model in calm water 11

3.2 Linear and nonlinear strip method for ship motions in waves 12

3.3 SMS - a platform for ship dynamic analysis 13

3.4 The near future development of SMS 16

4 Study of some dynamic stability problems of RoRo-ships 19

4.1 Roll motion due to the GM-variation of a RoRo-ship in waves 19

4.2 Probabilistic study of effective roll angle 22

Si Improvement of RoRo-ship safety at sea 24

References Appended papers: Paper A Paper B Paper C Paper D Paper E Paper F ._. . ... .... ... .. .

1 Introduction

A ship's dynamic stability problems in waves are in the most cases associated with roll or heel motion subjected to external or internal exciting moments, such as a wave exciting moment, a heeling moment from cargo shifting or wind pressure over the superstructure. Because environmental conditions govern ship motions at sea, structural strength and stability safety are design priorities enabling a vessel to withstand severe sea conditions throughout her

service life.

When roll motion is considered, one spontaneously thinks of the most

dangerous case of a ship's resonance roll motion subjected to a wave exciting moment, when an encounter frequency coincides with the ship's natural roll

frequency. This problem is mostly considered in the study of dynamic

stability, because most conventional ships have such construction

characteristics that resonance roll motion can easily occur.

However, the construction characteristics of a RoRo-ship are essentially different from a conventional ship in the following aspects:

large flare above the water line fore and aft with a fine hull form under the water line,

large beam to draught ratio and consequently a high mass centre usually above the wave line, which means that a large cargo space is available above the draught line.

relatively high speed,

almost full breath main deck.

The benefit of the RoRo-concept is that relative low density cargo such as

trailers, cars and other semi-fabricated or high-value products can be

efficiently loaded on and off for quick transport, enhancing competition in the transport market with other types of cargo vessels.

Consequently, a RoRo-ship has the following points of dynamics which are substantial in comparison with conventional cargo vessels:

A RoRo-ship has a low natural roll frequency between 0.3 to 0.45

rad/sec, while the natural roll frequency of a conventional ship is usually greater than 0.5 rad/sec.

A considerable magnitude of GM-variation in waves relative to the initial mean GM can be expected, due to the large BIT ratio in combination with the large flare fore and aft.

That the roll motion is strongly coupled to sway, heave, pitch and yaw motion due to the high mass centre and fine hull form.

Course instability problems may readily occur with this type of vessel. Load shifting can cause a large heel angle due to the transversely open

deck.

A RoRo-ship may then be subjected to such dynamic stability problems as: (i) resonance roll motion in quartering waves, (ii) loss of stability in quartering

and following waves, (iii) parametrically excited roll motion in waves, (iv) coupled course instability and roll motion in waves, (v) collision against other ships or marine constructions resulting in severe damage, dynamic stability problems with consequent losses, (vi) severe consequences due to cargo shifting; in the worst case there can be a total loss.

According to the statistics of the ship classification society Lloyds Register, there have been 72 RoRo-ships subjected to different kinds of damage during the period of 1980-1994 with over 2500 lives lost. In Europe, numerous capsizing accidents have been reported. Among those are: Zenobia, Herald of Free Enterprise, Vinka Gorthon, Jan Heweliusz and recently the Estonia. The RoRo-vessel is a relatively new type so the technical aspects of her accident mechanisms present an important subject for discussion. No ageing problems are observed in capsized RoRo-ships, which often occur in other vessels. In fact, dynamic behaviour is often the governing factor in most capsize incidents.

2 Analysis &some capsize incidents

The history of ship technique over hundreds of years shows that accumulated experience and knowledge play an important role in the evolution of ship construction, not only for successful designs but also for failures. A simple example is the IMO's intact stability criteria based on the statistics of GZ-curves in seaworthy hull forms and capsized forms. The development of regulations of ship classification associations is an another example.

Usually, some kind of official or unofficial technical investigation takes place after a capsizing. Due to considerable economic interest, different partners

involved in goods and passenger transport, such as ship owners, goods

traders and their insurance companies etc., have their own partial interests in the investigation, as opposed to a neutral investigation by a governmental committee.

Actually, the conclusion of an investigation is entirely dependent on the investigator's practical experience and theoretical competence. Of course, availability of model experiment facilities and analysis tools in terms of advanced computer codes are also crucial in a thorough investigation. The usual problem is getting reliable information about the circumstances, such as weather and sea conditions, human reactions during the capsize scenario

etc. As a matter of fact, each incident has its own particular circumstances, for a capsizing has the features of a chain reaction, in which several factors are interrelated and interacting.

The available information always contains some uncertainties; calling for an investigator to identify the true situation by means of the tools available to present a logical and consistent picture of the capsize scenario. A successful analysis of a capsize incident means that one looks at the problem from many

different aspects. Where ship dynamic problems are concerned, many

parameters such as environmental factors in terms of weather and wave

conditions, loading conditions of the ship and her dynamic properties,

human factors etc. have to be considered. All those parameters effect in different degrees the whole scenario. Apart from the quantitative uncertainty of those parameters, there are variations in different degrees. Identifying the degree of these effects in an incident scenario is a time-consuming task which requires, not only adequate analysis methods and an available high

speed computer, but also relevant knowledge and competence in the field. Evidently, the 'investigator's View of an incident has a governing role in the analysis. It often happens that different investigators have varying views of the same incident and hence different conclusions may be obtained. In this context, investigations can be carried out by the partners involved, in spite of their own partial interests. Discussions from different points of view are helpful, thereby a plausible if complex conclusion may be put forward, with

possible benefits for the general purposes of ship safety at sea. Such a

conclusion may reveal the possible weaknesses in the construction and the management of the actual vessel, providing knowledge for improvements thus preventing similar incidents, by raising the crew's consciousness of the

risks as a consequence of serious mistakes.

,2.1 Capsizing of "Herald of Free Enterprise"

On Friday 6th March 1987 the RoRo-passenger/vehicle ferry" Herald of Free Enterprise " capsized outside the breakwater of Zeebrugge on her route to

Dover.

The technical aspect is that the capsizing scenario, was probably less than one or two minutes as follows;

The bow doors were left open when the ferry departed from her

berth in Zeebrugge in a head trimmed condition. That made it possible for water to obtain ingress to G deck as her speed reached a critical level.

ID. A short time after passing 'Zand 1' buoy, see the map outside the

outer breakwater, Fig.3 in paper A, the quartermaster reported that he was having difficulty handling the ferry as she was not

answering the helm.

The ship was turning to starboard in spite of a hard port helm,

meanwhile the ship heeled rapidly to port. According to witnesses, there;

was, water on G deck before the heeling started.

,,She capsized on her beam and finally grounded about 800 m starboard from the route with the bow heading nearly 180 degrees off course.

The rapidity of the capsize incident is unusual and can evidently be

recognised as a dynamic process. An extensive investigation was carried out by British Maritime Technology shortly after the accident and reported in /6/ that the scenario was separated into two stages; first a rapid heeling motion caused by G deck flooding and thereafter turning to starboard due to the sheering off effect as a consequence of the large heel angle of about 25 degrees. Two separate mathematical models were created for these stages by

Dand with the capsizing scenario analysed by means of time-domain

simulation.

The roll motion can be strongly coupled to its turning motion, particularly for a RoRo-ship, because of its high mass centre and large beam to draught ratio.

This phenomenon is studied both experimentally and theoretically /121 by

Hirano and Takashina. This coupling effect is taken into account in the

theoretical investigation carried out by Hua in Paper A by formulating the motion equation for the capsize description, which includs surge, sway, roll

and yaw motion simultaneously, based on Ogawa and Kasai's modular

model. Their model is proved useful for RoRo-ships in model - and full scale measurements according to /32/ and /21/.

An important factor is the effect on the heeling motion of the water volume accumulating on G deck. By assuming quasi-equilibrium, i.e. the water surface remains horizontal in spite of the ship's motion through any degree of freedom, the heeling moment of the water on G deck can be calculated

approximately by

K, = - 0.529 . (1- tan" 0), tana

2

tan-Gg tang) -p- g

Here V, is the water volume on G deck as a function of time, a is the trim angle and Gg is the distance from the volume centre to G deck.

The calculated result for one case is satisfactory in comparison with one produced by the computer code BMTFLOOD being practically identical, see

Fig.11 and Fig. 18 in /6/.

Extensive time-domain simulation of the capsize model is performed in order to identify the effect of the parameters for the initial condition. These include the quantity of water on G-deck before heeling, the rate of ingress, the current

effect in terms of initial drift angle, and the ship's speed on the capsize

process. The results show that the ship heeling process displayed various modes dependent upon altering initial conditions. Some of them capsizing but not in all the cases. It also shows that the capsize scenario could take place within 40 seconds.

Before formulating a plausible description of the probable capsize scenario based the simulation results, one has to interpret the capsize circumstances into the initial conditions for the time-domain simulation. The interpretation could be controversial, because witnesses among the survivors may give conflicting evidence. Therefore only corroborating witnesses should be given priority.

At the time of the accident a current of about 1 knot was likely to have been running from roughly south-west to north-east. In combination with the forward speed, the current could result in a hydrodynamic moment forcing the ship to starboard. According to witnesses there was water on G deck before heeling started, which endangered course stability.

Accordingly, it could be deduced that the ship was engulfed having reached a critical speed at the beginning of the capsize, leading to uncontrolled turning to starboard, creating a centrifugal force to port forcing the ship to heel to port with the accumulated water on G-deck adding to the heeling moment. The scenario then took place with a domino-effect, finishing within seconds. The computation with realistic initial conditions shows that the incident could occur within about 30-50 seconds with an ingress rate of less than 10 ton/s. As a comparison, a 30 ton/s ingress rate used by Dand in /6/ in the simulation for the heel motion only, forced the ship to remain at a heel angle of 25 degrees. The systematic computation shows that the effect of heeling and

turning considering the amount water accumulated on G deck, plus the

ingress rate during capsizing, accounts for the speed of the incident.

2.2 Capsizing of the FtoRo-ship " Vinka Gorthon "

"Vinka Gorthon" specialised in the transport of paper-products from Sweden to the European Continent. In 1988 the ship encountered a moderate sea off

m is cargo mass and f roll angle. y and z is the horizontal and vertical

distance from the roll axe.

control was lost when the main engines stopped. After several hours of

floating, the ship finally sank, breaking an oil pipe-line on the sea bed.

Wave conditions were not so severe according to the Dutch weather service KLM, nor were violent ship motions experienced by the crew. The roll motion

amplitude was observed to be about 4-5 degrees.

Certainly, the cargo was not appropriately lashed. A full-scale experiment onshore was later carried out to determine the lashing system functionality. Results show that cargo shifting could take place at a static heel angle of

about 16-17 degrees, which is far beyond the observed roll amplitude.

A combined sea caused the incident with a wind wave accompanied by a swell propagating from another direction. The ship was subjected to the wind wave from the beam, with a swell from astern at an angle of about 30 degrees

to the wave. Calculating by means of the extraordinary strip theory shows that the wind wave caused considerable vertical and horizontal acceleration

while the roll motion was induced by the swell.

Cargo is exposed to roll motion, vertical and horizontal acceleration

simultaneously. Consequently, not only gravitation force but also force of inertia act on the cargo. So the equivalent roll angle was defined see ( 2.2.1 )

and used as a parameter to judge the risk of cargo shifting. The equivalent roll angle has the same effect on cargo as it lies on a heeled plane at an angle of the same magnitude.

The definition of effective roll angle:

=arcran(±iJ ( 2.2.1)

where;

F=m.(a%. sin 0 + an cos 0 0+ g sin0)

N=m-(a, cos 0 a, sin 0 + y + g cos0)

F: tangential force N: normal force

Fig.2.2.1 The forces on cargo due to the simultaneous effect of

vertical, horizontal acceleration and roll motion.

For an analysis of the capsize, the Monte-Carlo simulation technique in combination with the linear ship motion theory are applied by the authors for

simulation of the simultaneous effect in the actual wave condition. The

computation result shows that the probability of the effective roll angle

exceeding the critical value is sufficient to confirm the simultaneous effect of cargo shifting.

2.3 Capsize of "Zenobia"

During a demonstration of the function of the autopilot on 2nd June 1980, Zenobia was subjected to an uncontrollable coupled heel and turn motion, cargo shifting took place immediately causing a 40 degree heel to port. Five days later Zenobia capsized outside Larnaca after unsuccessful attempts to right the ship. Weather conditions had no effect on the incident.

On the 14th February the same year, cargo shifting induced by a severe sea,

caused the ship to heel about 40 degrees.

The capsize was analysed by the Swedish board of accident investigation, the basic factors causing the capsizing are;

The stability marginal of the ship was too low for the actual load conditions on 2nd June 1980 causing dangerous heeling behaviour during a turn at full speed.

Cargo lashing was faulty as the freight was not secured for an unexpectedly large heel angle.

The action of righting the ship was inappropriately performed with consideration to the configuration of the ballast tank system.

An examination of Zenobia's lines reveals that the ship has large flare fore

and aft, large BIT-ratio, sharp bow under the water line and twin skew

configuration aft. The hull form seems extraordinary regarding its stability characteristics, i.e. GZ-curves at some load conditions. Fig.2.3.1 shows the GZ-curve at a certain load condition, on which the meta centre height is sufficiently large at initial heel angles but very small in the range between 5 and 20 degrees. As a matter of fact, this feature of GZ-curve is not at all

Fig.2.3.1 GZ-curve of Zenobia

Therefore, it was found valuable to re-examine the dynamic characteristics of Zenobia in general, using available seakeeping theories and computer codes. A study carried out in /13/ by Hua in 1990 covers four types of dynamic

problems;

the coupled heel/yaw motion during manoeuvring

stability loss in following waves

parametrically excited roll motion

the simultaneous effect of the wave induced motions on

the cargo.

The basic mechanisms behind the two occasions of cargo shifting are

successfully explained. It is revealed that ships having the hull form and main particulars similar to Zenobia's are at risk from dynamic instability problems in both calm water and waves. This work shows that modern ship dynamic theories together with computer applications are powerful tools for the evaluation of a ship's dynamic characteristics qualitatively and to some extent quantitatively.

3 Development of analysis tool

Generally, a ships dynamic behaviour can be considered as the output of a

dynamic system where the input are external exciting forces from the

surrounding water, wave and wind pressure on the superstructure, steering

control etc. Depending upon the problem, this dynamic system can be

described in different degrees of complexity. Considering the hydrodynamic

aspect,

different mechanisms are involved such as the effect

hydrodynamic inertia, free water surface effect, lifting surface effect and

viscous effect etc. The forces induced due to these effects follow different scale

laws. Therefore, using only model measurement is not sufficient, since a good insight into motion mechanisms is usually required for a reasonable interpretation of the measured results. Regarding capsize investigation, it is extremely difficult to carry out model tests to repeat the exact scenario in a

time sequence corresponding to the real one, because the factors and

parameters affecting the capsizing are difficult to quantitatively determine, and more difficult to be arranged physically in a scale model, e.g. cargo shifting usually occurs during capsizing and plays an important role in the vessel's total loss.

Logically, utilising mathematical models based on first principle physics and verified by model experiment is the most efficient approach for capsize analysis.

3.1 Ship manoeuvre model in calm water

There are several approaches for describing a ship's manoeuvring

characteristics such as the following three main categories: Input-output relationship models.

Holistic ( called also "Global" or "Regression " ) models,

Modular manoeuvre models.

The development in the field of ship manoeuvring favours modular

manoeuvre models, which reflect to a high degree the physics of manoeuvre motion mechanisms achieving comparable results to full scale trials.

An important part in establishing a modular model is to determine the

hydrodynamic forces on a ship's hull during the plane motion. Manoeuvre motion in calm water is characteristically a kind of slow motion in time perspective. It can therefore be treated as a quasi-steady motion in theoretical modelling for the calculation of hydrodynamic forces on the hull. Slender ship approach has been successfully adopted for the calculation of the linear part of the hydrodynamic forces in terms of linear hydrodynamic derivative, and shows good agreement with model measurement, see /22/, where the

effect of trimmed condition is also evaluated. The nonlinear part is

determined as a viscous effect of the cross flow.

Actually, the most difficult problem in the mathematical modelling of a

ship's manoeuvre motion is to determine the hydrodynamic interaction

between the rudder, the propeller and the aft body, which is the basis for calculation of the rudder forces and forces on the hull due to interaction. This problem is discussed in detail by Ogawa and Kasai in /36/ and commands great attention as a research subject in recent years. Semi-empirical methods for calculation of the rudder forces are usually used.

3.2 Linear and nonlinear strip method for ship motions in waves

The fifties saw a development of ship seakeeping theory. A stochastic model for irregular seas was established by W. Pierson, Jr. in 1952, by introducing spectrum representation. A year later a unified linear seakeeping theory for ship motions in irregular seas was established as a result of the collaboration between W. Pierson, Jr and St. Denis.

The concept of linear strip-method for calculation of ship motions in regular waves, introduced by B.V.Korvin-Kroukovsky, /27/ and /28/ in the middle

fifties became a successful numerical approach as a frequency-domain

solution based on the two-dimensional calculation of added masses and damping coefficients. For conventional ships, the calculated wave-induced motions and wave loads on the hull by the strip approach are generally in good agreement with model- and full-scale measurements.

The great advantage of the strip-method is the relatively numerical

simplicity, facilitating extensive calculation without demanding large

strip-method can some times match those based on 3-dimensional hydrodynamic calculations.

The linear seakeeping theory is an attractive model for practical use, having the following basic theoretical assumptions with respect to hydrodynamic calculations:

high encounter frequency or Xe/B-1

small magnitude of motion amplitude in relation to hull geometry side wall

limited forward speed,

However, this model is still available for conventional ships in moderate wave conditions, even in the range of low encounter frequency. The reason is that the hydrostatic and Froude-Kryloff forces are dominant and govern ship motions in this range.

An extension of the linear model is to calculate the hydrostatic and

hydrodynamic forces by taking the momentary wetted hull surface into

consideration, but still with strip approach. This is a nonlinear strip

approach in the time domain. For ship motions in severe wave conditions, this approach is appropriate for analysis of some dynamic stability problems in following and quartering waves. It is also available for calculation of high speed ( even in planing conditions ) ship motions in heading waves and wave

loads.

3.3 SMS - a platform for ship dynamic analysis

Paper C is a description of a computer code SMS for ship dynamic analysis. Development of analysis methods has taken place continuously during the past 8-9 years in connection with the author's research activity in analysing practical dynamic problems. In 1986, the linear seakeeping theory for the calculation of wave-induced linear responses such as ship motions, wave

loads etc.

in regular, long- and short crested irregular waves, was

formulated into a computer code named SGENS, based on a code developed by

Miao in 1980 for the calculation of ship motions in regular waves; developed

from the extraordinary strip theory formulated by Salvesen, Tuck and

method, a so-called "Frank's close-fit method", /7/ was programmed and integrated with SGENS. SGENS was extensively utilised for investigation of the simultaneous effect of ship motions on cargo shifting as occurring on "Vinka Gorthon".

A manoeuvre motion model of modular type proposed by Ogawa and Kasai,

see /36/, was formulated in 1987 in computer code by the author for an

analysis of the capsize of the "Herald of Free Enterprise", see Paper A. The hydrodynamic derivatives were obtained by using the formulas and statistics from model measurements as a function of main hull particulars from /32/

by Motora and /21/ by Inoue et.al.

Because seakeeping problems usually occur in large amplitude waves,

different kinds of nonlinearity have to be considered. Therefore, time-domain simulation methods should be used instead of the linear frequency-domain analysis. In 1988, work started for a code development based on a nonlinear strip-approach. In /15/ by Hua, the main feature of the mathematical model is described, following Fujino's work in principle, see /8/. The following nonlinearities are taken into account:

Froude-Kriloff forces are calculated by integrating the hydrodynamic pressure due to the incident wave velocity potential over the momentary wetted hull surface.

Sectional added and damping coefficients are calculated for the momentary wetted sectional form.

Nonlinear radiation and diffraction forces are calculated according to the " Fluid momentum theory ", which implies that flare slamming is automatically evaluated in the procedure.

Hydrodynamic coupling effects between sway, heave, roll, pitch and yaw due to momentary wetted asymmetric hull forms are taken into

account.

The nonlinear model of manoeuvre motion is superposed onto the general model.

During the work, a code for time-domain calculation of two-dimensional

hydrodynamic transient problems, associated with large amplitude motion,

was implemented based on the boundary element method developed by

Chapman in 1979, /3/. However, this code was not integrated into the

nonlinear strip model due to the limited computer power at that time.

SMS is the abbreviation for Ship Motion Simulation for Practical Application, with a Pascal code for general time-domain simulation of ship motions in

calm water and in waves, see Paper C. Most numerical procedures are

translated from the Basic code developed during the previous works. SMS has a modular structure consisting basically of a number of standard calculation

procedures. As a research and development tool for analysis of ship

dynamics, SMS is structured so that it should be easy to implement different mathematical models, serving two purposes. One is for the development of new or more accurate mathematical models, e.g. for description of high-speed ship motions, while some of the standard calculation procedures are still available. The other is to extend an existing mathematical model with other functions for studying a specific problem such as combined effects of motion accelerations on cargo and cargo shifting, effect of cargo shifting, effect of hull damage and ingress accumulated within the hull structure in

the ship capsizing scenario, non-linear wave loads on hull structure or

slamming impact force.

Up to now three mathematical models have been implemented in SMS. They are for the ship manoeuvring motion in calm water, the wave induced ship motions, and the turning motion in waves. The latest model is a combination of the previous two. All the three mathematical models are available only for

conventional monohull ships.

Generally, the time-domain simulation method is used in the context of dynamic analysis for the following purposes;

analysis of the complexity of dynamic behaviour of nonlinear

characteristics, for example large roll motion is strongly interacted with heave and pitch motions;

verifying the simplified models and determining the scope of their applications, e.g. a single nonlinear roll motion equation considering parametric excitation;

finding unknown ship problems, e.g. some dynamic stability problems where human factors are involved;

quantitative study, e.g. slamming impact due to the large relative

motion of the ship to wave surface.

3.4 The near future development of SIVLS

The analysis capability of SMS is restricted to conventional low speed

mono-hull ships in intact condition. Large high speed ships for transoceanic

service is the recent trend in the development of new types. Unconventional

hull forms such as planing or semi-planing ships, SES, SWATH and

trimaran etc., are the usually adopted concepts. Analysis of their dynamic behaviour requires three dimensional calculations for some hydrodynamic problems. Therefore, further development of SMS is necessary to satisfy the requirements.

Boundary element method, BEM, is an efficient approach for three

dimensional hydrodynamic calculations. A number of mathematical

formulations are available for different kinds of problems such as the

Neumann-Kelvin problem, determination of added masses and damping coefficients for linear seakeeping problems, linear seakeeping problems in the time-domain, i.e. evaluation of the hydrodynamic memory effect, and ship motions in large amplitude waves etc. Development of fast and accurate numerical algorithms are important for computation of those problems. For the Neumann-Kelvin problem, a fast and accurate numerical solution of the corresponding Green function is presented by Newman in /33/, /34/ and /5/. Hearn in 1977, see /11/, derived the Green Function into a finite integral

for a source of pulsating strength in water without forward speed, so

computation time could then be rapidly reduced. Thus, the added masses and

damping coefficients, plus the linear diffraction forces can easily be

calculated for a stationary ship or marine construction in waves.

For ship motions in waves with forward speed, the Green function used contains a double integral. The work presented in this field can be found in /2/ by Chang, /20/ by Inglis and Price, /9/ by Guevel and Bougis, /45/ by Wu and

Rapid development in computer technology facilitates seakeeping problem solutions in the time-domain. In 1987, Beck and Liapis published a three

dimensional computation of ship motions in waves in the time-domain

without considering forward speed, see /1/. King et al. in 1988 /26/ presented their computation result of ship motions in waves with forward speed.

Usually, time-domain analysis is used for studying dynamic instability

problems. So non-linear problems due to the large amplitude motions have to be considered. Lin and Yue in 1990 /30/ presented a time-domain solution, where the exact body boundary condition is satisfied on the instantaneous wetted surface of the moving body, while the free-surface boundary conditions are linearized.

However, it demands great effort to develop a general computer program for general purposes. In the initial stage, the work should be focused on building a program framework with appropriate input process, panel generation and post process. That serves as a ground for the development of a solution to

certain hydrodynamic problems in an actual research project.

As long as the computer power is limited, slender ship theory remains a practical approach to take into account the three dimensional effect on some hydrodynamic problems. Various solutions are available, e.g. for calculation

of linear seakeeping problems, drift force and moment in waves, and

hydrodynamic derivatives for ship manoeuvre motion etc, see /22/.

The linear wave model based on the superposition principle is mostly used in the studies of seakeeping problems. However, in a severe sea with short wave length, the nonlinear effect appears clearly. The wave crest becomes sharper and the wave dale more flat than the description of the linear wave model. Wave breaking can also take place as the velocity of the water particles in the vicinity of the wave top exceeds the wave propagation speed. This nonlinearity can certainly have significant effects on some seakeeping problems such as a

ship's manoeuvrability in waves in association with broaching-off, or

slamming impact.

Still, there are some problems in dynamics, which are difficult to solve

numerically.

Important are non-linear roll damping, ship resistance in

the effect of different rudder types on hulls. However, a lot of model and full-scale measurements have been carried out and the results are published in different forms. Therefore it is important and possible to establish data banks in SMS where systematically selected data may be stored.

4 Study of some dynamic stability problems of R,oRo-ships

Considering dynamic stability problems as applied mechanics, the research

aim is to identify the basic problem mechanisms, and furthermore to

determine the quantitative relationship between a ship's dynamic behaviour, sea conditions and dynamic characteristics.

For the safety of a ship at sea, it is essential for ship designers and ship

operators to have knowledge about relationships in concrete terms such as the effect of trim condition, the position of the mass centre, the ship's speed, the course angle in relation to the wave propagating direction and the wave parameters etc. on the dynamic behaviour of an individual ship.

It is unrealistic, not only economically but also practically, to perform

experiments in full-scale for qualitative as well as quantitative studies of dynamic stability problems in waves, nor is it easy in scale models because of the difficulty in measurements. However, numerous capsizing incidents occur every year and technical investigations show that dynamic instability

problems are the main sources of serious losses. Hence, providing

involuntary full-scale experiments, indicating at least the existence of the problems. Thus, mathematical models based on first principle physics is a practical and efficient way to study those incidents. The advantages have already been discussed in section 3. The following is a brief presentation of some theoretical studies, to understand in a general sense, dynamic stability

problems associated with RoRo-ships in waves.

4.1 Roll motion due to the GM-variation of a RoRo-ship in waves

Parametrically excited roll motion of a ship was observed by Froude more

than one hundred years ago. Interest arose early in the beginning of the

fifties to study this kind of problem. Kerwin /25/ investigated the GM-variation

of a ship model in longitudinal waves. It was a quasi-hydrostatic study

without consideration of the hydrodynamic effect due to the ship model motions in the waves. The result from numerical calculations showed a fair agreement with the measurement of the model. Paulling and Rosenberg /37/, studied the problem at the end_ of the fifties, by assuming that the variation of roll restoring moment of a ship is a result of forced heave motion of the ship in still water.

In recent years, a lot of basic studies have been carried out on this subject, with reviews of some works in Papers B and D. However, most of them are based on the so-called Mathius' equation with some modification, by taking

the nonlinear damping effect or the nonlinear restoring moment into

account. The results provide basic understanding of the characteristics of

parametrically excited roll motion, but are not sufficient to take the

complexity of dynamic problems into account.

As an example, Figure 1 in paper B shows the borderlines between the stable and unstable zones as a function of h and wokoe for different roll damping. However, the stability borderline in the figure is a mathematical definition,

demonstrating that the roll amplitude is limited within the stable border

area. But, it does not say how large the roll amplitude is. As a practical

problem, the acceptable roll amplitude is limited when considering the cargo lashing system where the allowed roll angle is usually about 30 degrees. An another question is how large the magnitude of a parametrically excited

roll can be, when the RoRo-ships are involved in the interaction between the

roll and heave or other motions, not taken into account in the Mathius'

equation.

In Paper B, computer-simulation has been used to study the behaviour of a RoRo-ship subjected to parametrically excited roll motion in longitudinal regular waves. The influence of parameters such as ship speed, KG-value, wave amplitude etc. on this kind of roll motion is investigated. One important conclusion is that the strong coupling between roll and heave motion may counteract an increase of the roll amplitude, which is why the amplitude in the time-domain simulation is limited, in spite of the fact that it should be unstable according to the solution of Mathius equation.

A further study carried out on the same RoRo-ship in Paper D, shows that parametrically excited roll motion can also occur in oblique regular and

irregular waves. Because it is time-consuming to make time-domain

simulation of ship motions in irregular waves, it was not possible to

determine their statistic characteristics. However, the results indicate that the roll amplitude due to parametric excitation does not become considerable in irregular waves. But, the time-domain simulation of the equivalent roll angle, the simultaneous effect of vertical and horizontal accelerations and

roll motion on the cargo, shows that large equivalent roll angle can be

induced, and can be dangerous with a serious risk of cargo shifting.

Some assumptions have to be made of the hydrodynamic aspect when

studying dynamic problems using a mathematical model. Regarding the problem of parametrically excited roll motion, it is appropriate to take into account only the forces due to wave excitation and reaction forces due to the wave-induced ship motions. The other forces are assumed to be neutralised by each other. In other words, ship speed and relative course to wave direction

keep constant during the time-domain simulation for a certain service

condition. The wave excitation forces consist of Froude-Kryloff forces and diffraction forces, and the reaction forces of restoring forces and radiation forces. Mathematical models in Paper B and Paper D respectively are based on the nonlinear strip approach. The two-dimensional added masses and damping coefficients were calculated using the ' close-fit method', developed

by Frank in 1967. The Froude-Kryloff forces and restoring forces are

calculated by integrating the quasi-hydrostatic pressure distribution, over the momentary submerged hull under the wave surface, which is corrected for the Smith-effect due to the incident wave potential. When calculating the radiation and diffraction forces in Paper B, the momentary submerged hull is taken into consideration and the nonlinear part of the hydrodynamic forces are calculated according to the fluid momentum theory, while in Paper D

only linear parts are calculated, considering the submerged hull at mean draught in calm water.

Determination of the hull form effect on the magnitude of GM-variation of a

ship in waves is important for analysis of the result from time-domain

simulations, and for the establishment of design criteria regarding dynamic stability problems. In Paper E, the author derives the GM-variation into a

function series with aspect to the variation order and uses the Volterra

system for its representation. Thereby the hull form effect can be explicitly described by series expressions, showing that large flare fore and aft and the large ratio of the beam to draught are the governing parameters, numerical results of the first order GM-variation show satisfying agreement with the simulated.

The conception of equivalent roll angle is defined describing the simultaneous effect of vertical and horizontal accelerations with roll motion. Actually, not only for cargo shifting risk, but also for fatigue damage of the lashing system,

motion induced interrupt and comfort-conditions onboard are strongly

related to this simultaneous effect.

In fact, the equivalent roll angle is a kind of non-linear response of a ship in

waves. According to the definition in (2.2.1), the nonlinearity is totally

dependent upon the magnitude of vertical acceleration. It is clear that the linear spectrum theory is not appropriate for evaluating the probabilistic characteristics of this problem in the case of large vertical acceleration. In paper F, an analytical expression is derived for probabilistic calculation of equivalent roll angle. A Monte-Carlo simulation technique is also described for calculating the same problem. Both methods are based on motion transfer functions, calculated according to a linear strip-theory of ship motions in regular waves. Results show that the methods are in good agreement.

The probabilistic calculation of the equivalent roll angle of a RoRo-ship is

carried out with the parameters of significant wave height, mean wave

period, ship speed and relative course angle etc. The calculation proves that the nonlinearity of the angle results in a magnifying effect at its extreme value, in the sense of probability, showing that a large peak value of the equivalent roll greater than 35 degrees may occur in severe wave conditions. The computation result, shows that the simultaneous effect becomes most severe in beam-bow waves even with moderate roll motion, because of strong correlation between the vertical and horizontal acceleration. In general. other ships have a similar feature as the actual vessel, where vertical and horizontal accelerations can become considerably large simultaneously at these relative course angles. Equally, the accelerations are proportional to the

encounter frequency in square, which becomes greater than the wave

frequency at these relative course angles. Usually, RoRo-ships have low natural roll frequencies so that the direct roll resonance may not occur to these ships in beam-bow waves. However, in bow waves RoRo-ships can be subjected to parametrically excited roll motion, shown in Paper E, where

large equivalent roll angle is expected and may become dangerous.

Another dangerous case occurs when a RoRo-ship encounters sea conditions of wind wave and swell in different propagating directions. According to some reports, at least 20% of sea conditions have the characteristics of a mixed sea. It can happen that the wind wave in a mixed sea encounters the ship from the bow direction, resulting in significant vertical and horizontal accelerations, while a quartering swell causes considerable roll motion due to the resonance phenomenon.

For bulk carriers, the risk probability is considerable when subjected to large equivalent roll angles in bow waves. Having relatively high natural roll frequencies, the direct resonance roll motion as well as larger vertical and horizontal accelerations can take place simultaneously.

5 Improvement of RoRo-ship safety at sea

The improvement of ship safety at sea is widely discussed for dealing with ship stability problems. A lot of constructive suggestions have been put forward in the following aspects;

modifying the existing international ship safety regulations improving design with better safety considerations

International legal enforcement for improving professional training and operative management

However, the development of international ship safety regulations is a long term feed-back process based on the accumulated experience of accident lessons. Ironically, it requires many years before a rational proposal becomes accepted and ratified by most nations in the world due to interests other than safety benefit. Construction design with better safety considerations is an

appropriate approach in this context, but is limited by economic

considerations regarding new-building investment and cargo handling

efficiency. Recently, a number of ship-operators have accepted the idea and are ready to improve their existing RoRo/passenger ships, after the capsizing incidents of the " Herald of Free Enterprise " and the " Estonia ".

In general, an accident occurrence is a consequence of the inter-action

between the actual ship characteristics, the environmental conditions and human fallibility. Accident investigations reveal that those three aspects are

closely inter-related. From the author's experience of the analyses of a

number of capsize incidents, human fallibility is usually expressed in terms of unawareness of the consequence of an irrelevant action or a less than careful decision, particularly where RoRo-ship incidents are concerned. Even though the Roll-on and Roll-off concept has existed for at least thirty years, knowledge is still much too limited concerning their in-service dynamic behaviour and the potential capsize risks in intact as well damaged condition.

Even more serious is that the available knowledge is not sufficiently

highlighted among the companies and crews in ocean transport practice. As the number of high speed RoRo-ships increases in service, dynamic

stability problems are expected to appear more frequently. Unfortunately, some of problem modes, such as resonance roll motion, roll motion due to stability loss in quartering waves or broaching-to etc. are difficult to avoid by appropriate construction design due to the RoRo-concept. As these problems occur only at specific times regarding environmental conditions, dynamic characteristics and human fallibility, I believe that a radical improvement of professional training and operative management are important aspects for consideration in RoRo-transport progress.

A total safety analysis of individual ships and operational guideline

Ships are very individual regarding size, hull form, load conditions and service speed. Consequently, dynamic characteristics are dissimilar with variation in dynamic behaviour as well as dynamic problems. It is not self-evident that a ship operator having good experience of a particular vessel can still operate another one with the same skill.

Progress in the scientific ship research during the past forty years shows that there are several approaches available for the determination of dynamic

characteristics and behaviour of a ship in waves including model

measurement and/or theoretical calculations. Many dynamic problems can today be more or less accurately calculated with the computation power of

even a moderately advanced PC-computer.

combination with

accumulated experience and knowledge and to some extent with model measurement, it is possible to make a complete analysis of the dynamic characteristics of an individual ship in order to examine its safety status. It is

very important that the crew of a ship are well instructed in emergency

procedures and trained to meet any possible incident with the most

appropriate action.

An operative guideline manual for ships can also be developed with better consideration to seakeeping aspects. This kind of manual can provide sound

advice on the correct choice of speed and course in all sea and weather

conditions to minimise the risk of dynamic problems. Weather route

Rapid development in computer technology now facilitates efficient

sophisticated algorithms. The key problem is still weather and wave

forecasting. The third generation WAM wave model is now fully operational at the European Centre for Medium Range ( 3-8 days ) Weather Forecasting ( ECMWF ), at Reading England. The fourth one is on course to be put into operation.

According to the recent state of the art report from /39/, research progress in the development of wave models for wave growth prediction has reached such a stage, that they are able to routinely and precisely specify the space-time evolution of sea conditions on a global basis, when the promise of remote sensing, to provide accurate operational marine wind fields is fulfilled. We

can expect that in the near future, weather routes may be an important

procedure in seaborne transport.

The weather route is an optimal decision considering several objectives, e.g.

fuel economy, transport efficiency and safety level.

Onboard based surveillance system

A practical solution, increasing the safety level for ships at sea is to install a

surveillance/expert system onboard having different configurations

depending on its aim. It can be a kind of stress-monitor simply for surveying

the structural behaviour of a ship in waves. But it is also possible, with

regard

the

recent development of computer technology and

Weather and wave forecasting in combination with onboard motion

measurement may considerably improve evaluation accuracy. Thereby

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Journal of SNAJ, Vol.168, Dec.1990 "

" Herald of Free Enterprise"

by Jianbo Hun

Div. of Naval Architecture, Dept. of Vehicle Engineering Royal Institute of Technology, S-100 44 Stockholm, Sweden

Abstract:

A simplified mathematical model has been established for time-domain simulation of capsize scenarios for RoRo-vessels such as " Herald of Free

Enterprise ". The capsize can be studied as a consequence of the interaction

between heeling and turning motion. The influence of different parameters has been studied. The result shows that quantity of water on G deck before heeling, ingress rate of water, ship speed, hull form and KG-value are the

main parameters governing the capsize scenario.

Contents

Background 1

Mathematical Model 3

Result of Time-domain Simulation 7

Discussion 9 Conclusion 12 Acknowledgement 13 Nomemclature 14 Reference 15 ...

Background

On Friday 6th March 1987 the RoRo passenger/vehicle ferry " Herald of Free Enterprise " capsized outside the breakwater of Zeebrugge on her

route to Dover with heavy loss of human life. The capsize took place in less

than one minute. The ferry finally grounded about 800 m starboard from

the route with the bow heading nearly by 180 degrees off course.

" Herald of Free Enterprise " had a service speed of 22 knots. The main

particulars can be found in Tabel.l. Figure.1 shows the general

arrangement. The cargo in terms of cars and trailers rolled on and off

through the openings in the bow ( B/H 6.0m /4.9 m )and stern (B/H 8.5/4.73 )'.Vehicles were carried on D, E. F and G deck.

When departing from the berth, the ferry was trimmed by head and had the

bow doors left open. That made it possible for water to ingress to G deck as

the ship's speed increased. According to the witness there was water on G

deck before heeling started. The heel angle first stayed for five, six seconds

at about 20-25 degrees and thereafter the ship continued to capsize. In the meantime, the vessel was turning to starboard and could not be stopped in spite of hard port helm. Water flooded into the superstructure quickly as

the vessel went over on her beam.

Technical investigations have been carried out including time-domain simulations of different mathematical models, tank model experiments and full-scale measurements. Even if much valuable information has been gained a complete picture is still lacking. Among the questions are the

following:

How large was the quantity of water that ingressed to G deck before start of heeling and how large was the rate of ingress ?

What is the low limit of quantity of water on G deck required for capsize ?

The ferry was turning to starboard while heeling to port and come to rest on a heading very nearly opposite to that of her original course. How large was the maximum turning rate and how large was the effect of the interaction between turning and heeling on the capsize ?

How fast was the capsize ?

How did the ship reach its final position ?

Usually, when a ship starts turning to starboard she heels first to starboard due to the rudder force. Then after a few moments she heels to port. This is

because the lateral inertia forces, the rudder force and the lateral

hydrodynamic force act at the different levels so that a heeling moment can be induced, which we can call heeling moment of turning. Experimental measurements and calculation have been shown that the heel angle has a strong influence on the turning radius, see /1/. The turning radius decreases as the heel angle increases. Sequenntly the heel angle grows due to the

increased heeling moment of turning. This effect is apparent for ships of the

roll-on/roll-off type. Large beam to draft ratio and high vertical position of mass centre are considered to be the major characteristics of the hull which make the ship's turning moment sensitive to this phenomenon.

" Herald of Free Enterprise "had a GZ-curve increasing linearly with GM value of 1.7 m up to about 30 degrees heel angle and then decreasing down to zero at 57 degrees heel angle. The transverse stability was sufficient in normal cases and the phenomenon mentioned above was difficult to observe. However, as water had inflooded into G deck the transverse

stability would decrease more or less depending on the quantity of water on

G deck. When the ship was in upright position GM was reduced due to the free surface effect of the water on G deck. In heeled condition the water on

deck acted as a heeling moment which is a function of heel angle.

The mathematical model in /1/ where the coupling between heel angle and turning motion is taken into account, has shown good agreement with experimental measurement in spite of its simplicity. In this paper the turning motion equation has been extended by including the effect of water

on G deck. The capsize can then be studied as a consequence of the

interaction between heeling and turning. The purpose was to find possible circumstance which could have caused the capsize of " Herald of Free

Enterprise ", but also to discuss the significance of parameters in the motion

equations which are related to the water depth, the hull form and the

2. Mathematical Model

The mathematical model comprises four differential equations of motion;

surge, sway, roll and yaw motion. Heave and pitch motion due to increasing

water quantity on G deck are considered here to have less effect on the

capsize and will not be coupled into the mathematical model. The degree of

freedom of motions is illustrated in Figure.2. (the mass centre is supposed

to be located amidships )

The terms with subscript h are the hydrodynamic forces acting on the ship hull. The terms with subscript r are the rudder forces. Kw is the heeling

moment due to the water on G deck.

The longitudinal hydrodynamic force is as followed,

X=Mr u+M,vr

where M, is the added mass in x-direction, My the added mass in

y-direction.

The propeller thrust together with the resistance are expressed

approximately as follows,

-(VON).

X(u)=-1.p L

2 cosi3 (6)

where X/) is the resistance coefficient at the initial ship speed V,.

The lateral hydrodynamic force and moment are,

Y, = -M M x M ,(13,?) ₍₇₎

N =

(v+

I.-O=K+Kr+K

where J the added moment of inertia, x. the coordinate of the centre of lateral added mass, YhO,

N,,0 and N, are the lateral lifting forces as

functions of and 0. ?=rLIV is the nondimensional turning rate.

1

Y,)= 7)pLdV2

+Y,-71,1

No=pL2dV2.[K.0.0+1\100+N.,..?+NwP2?+

+Alpe; -13 -12

N,=p-L.2-d-V2 [No 0+1Vp(0),63+ffr(0)tii

The hydrodynamic derivatives in (5), (6), (7), (8), (9), (10) and (11) are shown

in Tab.2. They are obtained by using formulas and statistics from model

measurements as functions of main hull particulars according to /3/ and /4/.

The heeling moment consists of hydrodynamic inertia moment, friction damping moment, rudder moment, moment of the hydrodynamic force and

heeling moment due to the water on G deck,

Kb= Jr, Ba 0+ Y

(12)

The last term in (12) plus the rudder moment is called heeling moment of turning. B, is taken equal to 15% of the critical damping /1/. The rudder

moment is obtained according to 15/.

Table 1. Main Hull Particulars

126.1 m 22.7m 5.7m Cb 0.525 L/B 5.56 B/d 3.98 GM

1.7m