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Ocean Engng. Vol. 8, pp. 65-84.
Pergamon Press Ltd. 1981. Printed in Great Britain
A REVIEW OF INTACT SHIP STABILITY RESEARCH
AND CRITERIA
C. Ktio and Y. WELAYA
Department of Shipbuilding and Naval Architecture, University of Strathclyde, Livingstone Tower,
26 Richmond Street, Glasgow GI 1XH, Scotland
AbstractAn investigation on capsizing of a vessel in a seaway is of paramount importance
from the point of view of safety of life at sea. The present paper analyzes the major research efforts made throughout the world regarding intact stability and the establishment of stability criteria. Attempts have been made by the authors to draw conclusions from this analysis and to provide guidelines for future research efforts in the field of intact stability of ships.
I. INTRODUCTION
SHIP stability from capsizing has always been of crucial importance to ship designers, ship
operators and regulatory bodies, because it is a major design requirement and also the key factor in ensuring the safety of life at sea. This justifies the great interest ship stability has received from naval architects, ship operators, scientists and mathematicians for over a hundred years.
Throughout this period, numerous studies have been devoted to the various aspects
of the problem but the progress which has hitherto been achieved is by no means
satis-factory because of the complexity of the problem. For this reason it would be useful to
carry out a literature survey from time to time in order to highlight the progress of our
knowledge.
The present critical review is prepared with three main objectives in mind. The first is to provide a better understanding of this difficult problem by analyzing and summarizing the major research efforts which have been conducted all over the world. The second is to examine and evaluate the background and basisfor the existing stability criteria. The third is Co draw conclusions which could help those who require the findings of stability studies
and to serve as a guide to future research efforts. The following sections of this monograph_ . _
will be directed at meeting these three objectives.
The analytical and experimental research studies are classifittd under the three different categories of:
Conventional approaches; Theoretically based studies;
Experimental studies and correlation with theory. Each item will now be examined in turn.
2. STUDIES ON CONVENTIONAL SHIP STABILITY
Under this category it is assumed that the stability of the ship can be determined from its geometry and weight distribution. In other words everything is dependent on the shape
of he righting arm curve in still water. Although this isa very old concept and its usefulness
involves accepting a number of drastic
ations, it is still the basis of most existing
regulations. 65 Library Mekelvveg 2- 2628 CD Delft The Netherlands Phone: 31 15 788373 - Fax: 31 IS 781835 0029-8018/81/010065-20 502.00;0
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66 C. Kuo and Y. WELANA
The main assumptions behind this approach are: The buoyancy remains constant;
Any contribution due to kinetic energy or energy dissipation can be ignored; All types of excitation are of potential nature and stationary;
Coupling and other hydrodynamic forces can be ignored.
The use of the righting arm curve for judging the stability of the shipwas first proposed
by Reed (1868) but the application was due to Denny who presented the first standard
righting arm curve in 1887.
However, Moseley, in his attempt to relate thestability of the shipto its rolling motion,
did introduce the idea of "dynamical stability as far back as 1850. The name is perhaps
misleading because it involves only the area under the righting arm curve and not dynamics
as the name might have implied. According to Moseley, if the area under the righting moment curve, up to the maximum angle of heel, is greater than the area under the heeling moment curve up to the same angle the ship is then considered stable. The heeling moment is due to some potential external force and in this case the area under the curve is the work
done by either the restoring or heeling moment_ The main assumption behind this approach,
which is the basis of the so-called 'weather criterion 7 is that the actions of the righting and
heeling moments are potential. However, this will receive extensive discussion in
Section 5.2.
This idea was further developed by Pierrottet (1935). In a paper before the INA he
tried to establish rationally the forces tending to capsize the ship and proposed a limiting
angle at which the dynamic lever of the ship must be equal to or greater than the sum of the
work done by the inclining moments. This proposal was not accepted on a worldwide basis
because it was too restrictive on the design.
In 1939 Rahola produced his famous doctoral thesis. The studywas based on the results
of official enquiries relating to 34 cases of capsizing. His approach was to analyze the
resistive capacity of ships which were known to haye capsized and to collect data on
restoring moments of vessels that had not capsized and then to establish minimum values
of these restoring moments to ensure the safety of vessels against capsizing_ He concluded
that a maximum righting lever of not less than 0.2 m at an angle of not less than 300 and a dynamical lever of 0.08 in radian up to the angle of maximum righting lever would provide
sufficient resistive capacity for the ship. Rahola's thesis raised great interest throughoutthe
world because it was the first comprehensive study of its kind and because the method is fairly simple to apply as it does not require any computations so long as the statical stability curve in still water is known. That is the reason why many national stability regulations or recommendations still rely on this approach in judging the stability of their fleets. However, there are serious limitations to Rahola's method. These will be discussed more thoroughly in Section 5.1.
A typical paper on conventional ship stability was read in 1951 by Skinner. In thispaper
he considered three cases which may endanger the safety of small vessels. These are wave
heeling moment, adverse wind couple and shipping of water. In his study he plotted the
heeling and righting moments on the same diagram and compared the area under the two curves. From this information he concluded that the effect of shipping of water, although a
contributory factor, is insufficient in itself to cause loss and that cargo shift is unlikely to be
a basic cause of the loss of small ships in the fully loaded condition. In all his calculations, Skinner concentrated on the beam sea, which he regarded as the most critical condition.
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Following the same line of thought, Steel (1956) studied the effects of shift of cargo, water ballast and wind heeling moment on the GZ curve. He emphasized the fact that there is no comprehensive short cut to adequate stability, and that the type of ship, service, and nature of cargo as well as many other factors must be taken into account.
In Japan, Yamagata (1959) presented the findings of the research which led to the stability criterion adopted in his country and this is again a typical weather criterion. In his paper, Yamagata gave a list of the critical loading conditions at which the criterion must be applied and concluded that the restoring to heeling area ratio must be determined
empirically. Finally, he was not satisfied with the method and suggested that further investi-gation was required to improve the applicability.
In 1960, Wendel proposed that the uprighting and heeling moments should be balanced in a hydrostatic manner. In this method a stability balance sheet would be prepared for each vessel and the values of righting moments at heel angles of 30°, 45° and 60° are to be computed together with a set of heeling moments due to the various causes. These may include wind moment, free surface effect, turning moment, water on deck, icing, moments due to operational loads and the effect of the seaway on righting moment values. The
amount by which the righting moments exceed the heeling moments is the safety allowance. Although Wendel succeeded in explaining some capsizings by his balance method, the probability of simultaneous action of all the unfavourable negative factors affecting the stability or causing a dangerous-heeling is apparently very small.
A modification to Rahola's criterion was suggested by Norrby in 1962. His method used the metacentric height as a measure of the dynamic stability of the vessel. Norrby suggested that the metacentric height could be estimated on board the vessel by measuring the rolling period and using. Kato's formula for the radius of gyration. The stability of the vessel can then be checked with the help of a diagram giving the necessary metacentric height as a function of the displacement. From the practical point of view this method makes it easier for the ship master to check the stability of his ghip but basically it involves all the assump-tions and limitaassump-tions of the Rahola's approach.
In the United States, the U.S. Navy adopted the wind line criterion as described by Sarchin and Goldberg (1962). Under the combined effect of wind and waves, the ship is assumed to have an initial heel of 25° on one side. The criterion requires the area under the righting moment curve to be greater than the area under the heeling moment curve by a margin of 40%. This safety margin is intended to account for the effect of gust and calcula-tion inaccuracy. This criterion was criticized for the arbitrary "knockdown" roll angle of 25° while in other countries this angle was calculated by various formulae which accounts
for the actual form of the ship. However, from the extensive application of this criterion it can be described as successful in providing adequate stability for U.S. naval vessels.
In 1964 The Intergovernmental Maritime Consultative Organization (IMCO) started its investigation into the ship stability problem. The first few years of the IMCO efforts were devoted to the assembling of data on casualties that had occurred and on typical vessels which had been operating successfully. The emphasis was placed on the need for a simplified criterion. In 1968, IMCO completed its work and produced its basic stability criteria. The approach followed by IMCO was exactly the same as that proposed by Rahola and it was based on an extensive survey of various national stability regulations and on the statistical casualty records. Although IMCO followed Rahola's approach, it did not reject the other moment balancing approach and at the IMCO working group, which was formed
67
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in 1975, it was agreed that some form of weather criterion should be adopted as an interim solution (Thomson and Tope, 1970).
It will be noted that the present IMCO criteria are not completely satisfactory. Theyare
described by many people as'unreliable and insufficientrespecially in the lower sizerange, a
ship having a length close to 24 m and for vessels operating in the light condition (Miller
etal., 1975). These uncertainties were supported by several casualties -of vessels which have
satisfied the IMCO criteria, sometimes with an ample margin, but capsized in adverse
weather conditions. Examples of these casualties are given by Miller et al. (1975) and
Morrall (1979), and also in the discussion which followed Cox (1977). The approach used in developing these criteria will be discussed in detail in Section 3.1.
The stability of fishing vessels was also the subject of a paper presented to the RINA in 1968 by two IMCO technical officers, Nadeinski and Jens. The purpose of that paper was to give an account of the programme of studies, the work done and the results so far achieved by different countries conducting research into various aspects of the stability of fishing vessels. In the end the authors stressed the importance of the international
co-operation and exchange of information between different countries to arrive at acceptable stability standards for fishing vessels and to avoid unnecessary duplication and overlapping.
In the International Conference which was held at the University of Strathclyde in 1975, Tsuclui a presented a new method for treating the stability of fishing vessels. In his method, Tsuchiya disregarded the idea of stability assessment by simple geometrical stability standard such as minimum metacentric height and freeboard or the shape of the righting arm curve. Instead, he considered a number of factors which, in his opinion, are very crucial. These are the worst weather conditions, the maximum heeling moment caused by the fishing operations, the angle of vanishing stability or the downflooding angle, water trapped on deck
and the hard rolling motion of the boat in the irregular waves until the bulwark top immerses into the water. For each of these hazards he introduced a certain coefficient which should be calculated and plotted on a diagram as a function of the metacentric height and the freeboard. On these diagrams he defined the safe and the unsafe stability regions and he then presented some examples. In suggesting this approach Tsuchiya was aware that it ignores some dangerous situations such as oblique seas and heavy rolling in beam seas, but it was a good attempt at taking more factors into consideration.
A similar approach was also presented at the same conference by Dorinetal. (1975),
but it was difficult to compare the relative merits of two approaches because Dorin's paper did not contain any application to real ships.
In 1977 Cox presented the British Fishing Vessel (Safety Provision) Rules of 1975. The rules are exactly the same as for the IMCO criteria and are applicable to all vessels other than beam trawlers. For beam trawlers they require a 20% increase in the values of dynamic stability, GZ and GM, in order to take into account the forces induced by their method of trawling. In addition, these rules demanded that the effects of wind gust and water on deck should be included. A typical weather criterion was suggested to take care of the wind effect but the parameter values were not specified so long as they were "satisfactory". The effect of water on deck was taken into account by balancing the areas under the righting and water heeling moment curves in a static approach. While the paper does not present any new ideas, I, it does illustrate the difficulties involved in approving proposed safety measures and issuing official regulations.
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W1-....-A review of intact ship stability research and criteria 69 3. THEORETICALLY BASED STUDIES ON SHIP STABILITY
Under this category all the studies are aimed at relating the stability concept to the equations of ship motions. The ultimate goal of this approach is to devise a procedure for assessing the ship's stability from its motions under deterministic or stochastic environmental
conditions.
In its simplest form, the approach tries to draw ship stability conclusions from the application of the one degree of freedom differential equation of motion. For uncoupled ship rolling motion, the equation may be written in a general form as follows:
/ (44 I) D ((I), 1) R (9, t) = K (9,1) (1)
where q) is roll angle; q.), roll velocity; if), roll acceleration; t,time; !,the inertia term and a
function of and t; D, the damping term and a function of ep and t; R, the restoring term
and a function of q and t; K, the excitation term and a function of p and t.
Although this approach seems a logical step forward and better than the conventional approach, it does have its own limitations and there are also difficulties associated with its applications to ship problems. Essentially these can be discussed under the following
headings:
3.1 Mathematical modelling
The theoretical approach is dependent on mathematical modelling and all the assump-tions associated with its applicability to a given problem. As yet there is no real proof that an equation, of the form given by Reed (1868), represents a good model of shipmotion. 3.2 Non-linearity
The pitch, heave, yaw and sway motions can be treated fairly readily by strip theory and they are to a good approximation of linear nature (Salvesen et al., 1970). However, it is reasonable to assume that capsizing is always associated with extreme roll motion which is a sharply tuned resonance phenonemon and as such the motion cannot be regarded as of linear nature (Morrall, 1975). Instead, it is necessary to consider the effects of non-linearity and this in turn makes the whole problem extremely difficult.
3.3 Reliability of approximate solutions
Due to the non-lincarities as well as coupling in restoring and damping terms only
approximate solutions are available.Typical examples are the use of the perturbation analysis technique for predicting the non-linear roll response in regular waves (Wellicome, 1975; Wright et al., 1979) and the method of averaging and the harmonic balance method have also been employed for obtaining an approximate solution for the roll equation (Wright etal., 1979). Alternatively, the behaviour of the ship can be studied by examining the step by step history of the motion resulting from numerical integration simulation on a high
speed computer (Bovet et al., 1974). Although these methods do provide some hints on how ship stability should be judged from the motion point of view, one cannot consider this as satisfactory because when the equations of motion are severely non-linear there is no guarantee that approximate methods can yield reliable solutions.
3.4 Evaluation of coefficients
It is still difficult to obtain reliable expressions for the hydrodynamic coefficients such
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as added mass and damping. Any solution for the motion equation is strongly dependent on how one can accurately evaluate these parameters.
3.5 Practical application
Results obtained from this approach cannot be readily applied to practical problems by
those having no specialized knowledge. For many practising naval architects physical
meaning of this approach is not appreciated.
--All these difficulties have not deterred many investigators from researching into this field. Some of these efforts are briefly discussed here.
An early attempt to associate the theory of ship motion to the problem oftransverse
stability was made by Grim.
In 1952 Grim found that under certain conditions extremely heavy ship rolling may
result from a ship travelling in following seas. The excitation in this case is caused by the periodically changing shape of the immersed part of the hull as longitudinal waves pass
along the length of the ship. A periodic variation in the position of thecentre of buoyancy
will, in turn, lead to changes in the position of the metacentre and this is best illustrated by
Fig. 1 in which GM is a maximum when the trough is amidships and a minimum when the crest is amidships. Accordingly, there will be a periodic variation in the metacentric height GM with a frequency equal to the wave encounter frequency.
The importance of this so-called parametric excitation was emphasized in many papers, see for example, Grim (1952, 1954), Wendel (1954), Kerwin (1955) and Abicht (1975). Theoretical treatment is therefore based on formulating ship rolling motion in the form of
Mathieu equations.
A typical form of this equation is
where d2cp
+ (a
2 s Cos 2r) cp = 0 dr 3 a 4pgVGM, lv E2 2pg78GM s (0E2 (2)where is the displacement volume; 1 the virtual mass moment of inertia; p, the water
mass density; g, the gravitational acceleration; GM the mean value of GM (t); 5GM,
the amplitude of GM (t) variation; coE, the frequency of encounter; t, time and
r =
cot.A rigorous solution to this equation shows that, depending on the values of thetwo
parameters a and s, there are regions of stability and instability (McLachlan, 1947). A
sketch of these regions is shown in Fig. 2. The stability in this context is ina precise
mathe-matical sense, i.e. if small motion starts inside an unstable region the motion will build up. Practically, this does not necessarily mean that the ship will capsize because (2) is a linear equation and as the rolling angle increases the equation will become invalid. How-ever, the knowledge that a small motion could build up represents a "dangerous condition",
and this should be considered as a warning.
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A review of intact ship stability research and criteria 71
For small values of .s, instability occurs when the ratios of the encounter period (TE) to the roll natural period (T) are near 0.5, 1.0, 1.5, etc. The first of these regions is the most dangerous because it corresponds to the widest of the unstable zones and has the most rapid instability growth rate, see Fig. 2. When damping is included in (2) the unstable regions are shifted away from the a-axis as shown in Fig. 2. However, it should be noted that in an actual irregular seaway, this parametric excitation will be of much less significance. In the U.S.A., Paulling and Rosenberg (1959) investigated the problem of unstable ship motions resulting from non-linear coupling. They studied the coupled equations of pitch, heave and roll by expanding them in a Taylor series. They found that heaveroll coupling could lead to unstable motions. The instability did depend on the parameters predicted by the theory but the magnitude of the effect was only in fair agreement with the theoretical
results.
The effect of a seaway on the righting arm curve was recognized some 40 years ago when Kempf (1938) noted that the stability of a ship in a following or quartering sea could be re-dticed when a wave crest is amidships and increased when a wave trough is amidships as shown in Fig. 3. Wendel (1954), Grim (1954) and Paulling (1960, 1961) also made extensive investigations on this phenomenon and they tried to analyze certain ship casualties and stability problems in terms of these seaway-induced reductions in stability.The total effect of following sea on ship stability may be divided, as shown by Paulling (1961) into two separate effects: (a) Alteration of geometry of the immersed part of the hull; (b) Non-hydrostatic pressure distribution over the immersed part of the hull.
Apart from one attempt by Kure and Bang (1975), all existing calculations of the righting arm variations in a seaway have been carried out in the following sea condition because it is the simplest case to compute. In most cases the procedure adopted was exactly like that followed in poising the ship on the wave in conventional wave bending moment Lalculation when a trial-and-error process is adopted.
Kure and Bang's attempt (1975) was unique in that they divided the effect of quartering sea into Two components. One component was calculated exactly like the following sea case and the other took in its account the moment due to the difference in the wave elevation as the product of displacement, GM, and the wave slope corrected for the angle of incidence by the sine of this angle. However, this is not strictly true because the total wave excitation in quartering sea is generally made up of two components. The first is the force exerted by
the pressure in the wave without taking account of the disturbance caused by the presence of the ship, so this component represents the whole force under the assumption of the FroudeKriloff hypothesis. The second component is a contribution resulting from the diffraction of the waves about the ship. As pointed out by Vugts (1968) the second
com-ponent is very important and should not be neglected.
Recently Welaya (1980) was able to evaluate the time-dependent and non-linear restoring moment in a seaway using a newly-developed computer program. A fresh stability criterion was formulated and it can be described as an advanced moment balancing procedure that takes into account the effects of wave excitation and energy dissipation. The procedure as a practical ship design tool has shown great promise on application to three ship cases when it was possible to differentiate "safe" and "unsafe" vessel conditions. The research results confirmed that this method can replace the_classic weather criterion for assessing ship stability because it is richer in dynamic information.
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-Followng sea 60 rn . 0.4 0.2 00 0.6 0.4 0. f'S..?...175::,:rj . 4:17:,,70 .-, .:-'01`" ..::-..._ -:::.0,17.,...". --..., z-.... ....- *":.. -43,iZst 2.,:.,,. ...i,z-:.,:'ir-..:.... '7111'2'-'4-4.::. 4,.= 4.'":'-''"4.23- '' ' -:-4--`-- - ;, 4-,., Fully. loaded ---- Half loaded -- I 1 00 03 .04 ' -' 00 -I '
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.-05 -04 .-03 -02 -01 0.0 0i,". :02 S,, ship , -3:7'- 04 05'For most! of the operating time ships sail in an irregular tea envirOnnierit. It is thereforei not surprising to find the work Of St penis ancl:PierScifi (195) using probability approach to
Ship motions in random seaways in stability studies Since rolling motion in a random seaway is-Jr'itOchastic process, several attempts were made to derive some probabilistic motion. properties by analytical techniques Typical examples are the studies by de Jong: !
(1973), and Haddira. (1971, 1974 and 1976).
-. .
In Germany, .Abicht (1972), considered, the combination effect of the rolling motion of I the 'shiri and the oscillation Of the righting arms caused by Waves overtaking the -ship. His
result was a probability of capsizing. In spite of many simplifications, the method was
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The difficulties encountered when pursuing a probabilistic approach wcre discussed by Kastner (1975). He pointed out that the best way to judge the safety of a ship from capsizing would be to predict the expected roll motion extremes and their probability of occurrence. However, he admitted that this is quite a cumbersome task and the main reasons are: (a) The linear ship theory used for motion prediction which is based on the superposition
principle, cannot be employed because of the non-lincarities at large amplitudes. (b) In a random seaway there is no single deterministic capsize, but we arc faced with capsizing as a stochastic process. (c) Capsizines are rare events even in some severe stationary seaways
and are dependent on a number of ship parameters.
A review of intact ship stability research and criteria 73 -.4.
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74 C. Kuo and Y. WELAYA
In addition, it seems scarcely possible to include factors such as heeling moments in a proper probabilistic manner. Thus, even by adopting a probabilistic approach one cannot expect ship stability to be solved in the near future because there are still many difficulties which must be overcome first.
A fi_nhap rmach_in linking the stability of the ship to its motion characteristicswas
introduced by Kuo and Odabasi in 1974. They continued the same approach in 1975, and suggested that a method developed by Lyapunov in 1892 should be used as a basis for the assessment of ship stability. In this method the motion of the ship is regarded as stable
provided the amplitude stays within predetermined limits. The method is based on the
fact that a large class of differential equations can be treated by a generalization of the idea
of an energy function called a Lyapunov function. If the function is zero or greater than zero
and its total rate of change with respect to time is zero or negative then the motion is stable.
However, Lyapunov's method suffers from a major drawback in that there is no fully
deductive way of finding the efficient Lyapunov functions.
More recently, two other papers have been presented on this same subject, one by
Odabasi (1977) and the latest one by Ozkan (1979). A common criticism to bothpapers is
thelack_of any evidence to show that the theory can have practical applications to ship stability. There are also certain other difficulties in this connection because the word "stability" has different meanings for naval architects and non-naval architects, such as mathematicians.
Thom's catastrophe theory is another mathematical theory brought into ship stability application. The catastrophe theory is a new mathematical approach for describing the evolution of forms in nature. It is particularly applicable where gradually changing para-meters (such as forces) produce sudden effects. Zeeman (1976) used this theory to study ship stability by examining the behaviour of the metacentric locus and treating ship capsizing as a discontinuous catastrophic phenomenon. In contrast to our present experience the
results of this study indicated that as the displacement of the ship increases the ship becomes more susceptible to capsizing. Zeeman was able to explain the capsizing phenomenon of ships in the following sea due to the presence of the wave crest amidships.
The idea involved is undoubtedly attractive but there are a number of practical diffi-culties. Firstly, the metacentric locus is too complicated for ship forms to draw simple explanations. Secondly, there appears to be no way of introducing dynamics in the treat-ment. It is, therefore, difficult to forecast any future prospects for this approach.
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4. EXPERIMENTAL STUDIES AND CORRELATION WITH THEORY
The intact stability problem is sometimes studied by carrying out experiments on ship models either in the experimental tank or in open water. There are two reasons for carrying out such experiments. To check and verify results obtained from theoretical analyses and to simulate conditions which arc very difficult to model theoretically as for example, the behaviour of the ship in extremely heavy irregular waves.
Model tests are normally very expensive and time consuming. From the design view point, when the stability characteristics of a certain ship are investigated experimentally, such tests arc usually conducted after the design has been refined. Unless there is a serious design error, only minor changes are likely to be made. The experiments in such a case are useless because minor geometric changes rarely produce significant changes in a ship's seakeeping characteristics.
However, one cannot ignore the usefulness of the experimental results obtained so far by different research centres all over the world.
An early attempt was made by Baker and Keary in 1918 to study the effects of the longitudinal motion of the ship on its statical transverse stability. After testing six models with different forms, they found that there is a systematic variation of stability with speed in all cases. Finally, they concluded that the variation of GM is independent of the trans-verse angle of inclination and it is all due to the wave formation.
Broaching and surging in following seas were studied extensively by Du Cane and Goodrich (1962). They conducted surging experiments with a free-running model in regular waves. One of the interesting observations from these tests was the "capture" of the model on the wave surface. In this case the speed of the model, relative to the wave, is reduced to zero and obviously there will be no surging motion. This, of course, has a significant effect on the directional stability of the ship and consequently on its transverse stability.
The effect of waves on the transverse stability of the ship, as discussed in the previous section, was also investigated experimentally by Graff and Heckscher (1941), Arndt and
Rodin (1958) and Paulling (1960, 1961). Nulling conducted experiments on two Series-60 models to test his calculation procedure and to assess the effect of beam/draft ratio and freeboard on the transverse stability in longitudinal waves. He found that the effect of ship speed on stability variations was not measurable within the experimental scatter. With a wave crest amidships, Paulling obtained righting arms. only half the calm water values. The narrow, high freeboard models showed less pronounced stability reduction than did the wide models. Paulline concluded that the standard wave of length equal to the length of the model and a wave height equal to one-twentieth of length provides a reasonable basis for assessing the stability in waves. He also concluded that the assumption of a hydrostatic pressure distribution yields results sufficiently accurate for engineering purposes.
Between 1971 and 1974, a sophisticated test programme with free-running ship models
were carried out by Paulling et al. (1972, 1975) in San Francisco Bay. The models were
equipped with extensive motion recording devices and were tested under remote control in quartering and following seas. The most important contribution of these extensive model tests was the identification of three primary modes of capsizing. These are defined as:
Low-cycle resonance, Pure loss of stability, Broaching.
The first mode refers to a roll build up as a result of parametric excitation in following or quartering seas. The second mode is associated with the presence of the crest of a wave amidships for a sufficiently long time so that the vessel's stability is greatly reduced. Broach-ing is caused by directional instability of a vessel acceleratBroach-ing on the surface of a wave in which case the rudder could not hold the vessel on course and the dynamic effect of turning caused the model to capsize.
All measured data were stored on digital tapes for further evaluation. This is probably
now the most comprehensive data base available on capsize events (Abicht et al., 1977).
However, as was stated by Paulling etal. (1975), despite the amount of data collected, it
was not possible to obtain a sufficient number of capsize events for an accurate long-term statistical prediction of the stability limit for safety from capsizing.
In the early seventies the U.S. Coast Guard has sponsored a major project to develop
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intact stability criteria for towing and fishing vessels. The research findings of that project were presented in a meeting of the American Society of Naval Architects and Marine Engineers in 1976 (Amy et al., 1976). Experiments on four models representing the whole American fleet were carried out in calm water and in regular waves. In all the free-running tests in following seas, capsizing and extreme rolling were due to either a complete loss of stability
Lor to rolling at frequency equal to half the wave encounter frequency. The experiments
came to emphasize the effect of water trapped on the deck in assisting the capsizing to
occur. Based on the model test results and other analyses they formulated a set of specific
intact stability criteria based mainly on the statical stability curve. In spite of the amount of valuable experimental work presented in that paper, the final conclusions as well as the proposed criteria themselves were not well validated. I.
Other examples of experimental work related to the subject of ship stability are the experi-ments of Dudziak (1975) in which he investigated the effect of beam waves and wind on the rolling motion of the vessel, and by Morrall (1975) where an experimental and analytical investigation of capsizing in beam seas was carried out for a side trawler.
Attempts were also made to reconstruct real casualties experimentally. In 1975 Kure and Bang presented a paper about the capsizing of a Danish coastal tanker in quartering sea, and in 1979, Dahle and Kjaerland described the experiments they conducted to
recon-struct the capsizing of a Norwegian research vessel in breaking beam waves. Both vessels
were in the ballast condition and satisfied the IMCO criteria. A common conclusion was that the IMCO stability requirements are not sufficient to prevent capsizing in certain sea conditions. The same conclusion was also drawn by Morrall (1979) after conducting
experiments on two models of small fishing vessels.
However, it is doubtful that a reconstruction of real accidents is of practical use because it is very difficult to take into account all the factors which existed at the time of loss and this is particularly true when ships are lost without survivors.
Having reviewed all these research efforts, it seems now helpful to look more closely
at the existing intact stability criteria, the basis of each approach as well as their advantages
and disadvantages.
5. A CRITICAL REVIEW OF THE EXISTING TYPES OF STABILITY CRITERIA
The target of every research into the problem of intact stability is to develop a set of
criteria which hopefully will enable the ship to operate safely and avoid any capsizing
-hazards. This is, however, a very difficult task because it is impossible to cater for all the
causes of loss by a single set of criteria. In addition, stability criteria sometimes contradict
other ship design requirements because stability is only one aspect in the whole design
spiral.
In practice, stability criteria are customarily divided into three categories (Bird and Odabasi, 1975):
Criteria based on setting the minimum limits for some of the ship parameterslike
the metacentric height or the freeboard.
Criteria based on minimum limits and requirements for the righting arm curve, e.g. the initial metacentric height, the area under the curve up to certain heeling angles and the values of the righting arm at selected positions on the curve.
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(c) Criteria based on the comparison of the areas under the heeling and righting moment
curves. This is commonly known as the weather or windline criterion.
The first two categories can be grouped together under one heading, the "statistical approach", while the third category is normally designated as the "physical approach". 5.1 The statistical approach
As was mentioned in the previous section this approach is based on the results of casualty statistical analysis. The minimum required values of the main parameters defining the righting arm curve, as shown in Fig. 4, are obtained from the histograms of the above-mentioned analysis. Certainly one reason for the continued application of this approach is the small calculation effort required to use such criteria. In addition, the advantage of any statistical approach is its ability to include all model and full-scale experience using suitable regression methods. However, attention must also be drawn to the following points:
Dearth of casualty data. The dearth of quantitative casualty data is one of the
major drawbacks in this approach. Indeed the available data constitutes only a small number of vessels. This makes the statistical analysis unsatisfactory because the sample size will
not be statistically significant.
Inaccuracy of the data. In a case where casualty data are available, it is generally not accurate enough because when the ship is lost it may also include the loss of all hands. Even if there are survivors, it is difficult to establish the exact reason of the accident. Hence, casualties included in the sample may not necessarily be due to loss of intact stability.
Imco stability criterion
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. .c;.. s"" ry.i."' '7'.**4-' %,`"g.,-Dissimilarity of ships within the sample. Within the sample, types and sizes of the
vessels may vary widely. Not only sd, but also in this approach ships withsharply different
projected lateral area are placed under the same category. Empirical data derived from statistics of casualties are useful only for ships that are similar.
Loading conditions are different. The loading conditions of the vessels included in the sample are different. In addition, the loading condition of the vessel at the time of loss is generally unknown. The resulting criteria, therefore, do not suit everyloading condition of the ship.
Environmental conditions are ignored. The environmental conditions for each
casualty are different. These are also completely ignored in the resulting criteria. Hence,
when the criteria are applied the ship is said to be safe or unsafe in an absolute manner without specifying any sea state or weather conditions.
Possibility of capsize of existing ships is overlooked. From the casualty analysis
carried out by Thomson and Tope (1970) on 68 dry cargo ships and 38 fishing vessels,
they found that half the casualties were experienced by ships more than six years old. This
indicates that a ship may become a casualty after years of apparently safe operation, i.e.
the fact that some of the existing ships might become casualties in the future is overlooked in this approach.
(g)" Unsuitability for new designs. Nowadays with the variety of newly developed ship
designs, with no experience and insufficient statistical information, continued reliance on
past experience may result in criteria whose applicability becomes less and less reliable. A good example was given by Amy et al. (1976) about supply vessels. These are relatively of conventional form, and yet experience has shown that it is not always possible to ensure their safe operation using criteria developed and tested before the introduction of these
vessels. Hence this approach is inflexible because it cannot be extended to ships ofnew
types.
(h) Unreliability of resulting criteria. From the application of criteria resulting from
this approach, such as IMCO criteria, it does happen that ships satisfying these criteria with an ample margin do capsize and ships not satisfying the criteria at all survive. Examples of such ships are given by Miller et al. (1975) and Bird and Odabasi (1975).
5.2 The physical approach
In this approach it is generally intended to provide sufficient stability for the ship to withstand the external forces, such as wind and gust, acting upon it. As shown in Fig. 5, this approach can be used to tackle two dangerous situations (U.S.S.R. Delegation, 1971).
The ship is heeled in calm water under the action of a constant or squall wind, Fig. 5a. This allows the evaluation of the wind resistability of a ship. Practically this situa-tion may occur very seldom because strong wind is always associated with the presence of sea waves and consequently some rolling motion. However, it should be noted that this kind of criterion is currently being used by the classification societies to assess the intact stability of semi-submersibles, e.g. American Bureau of Shipping Rules for Building and Classing (Anonymous, 1973).
The ship is rolling under the effect of wind and/or gust forces, Fig. 5b. This isa
possible situation during the:operation of any ship. As was described by Kure and Bang (1975) the roll motion commences from the initial heel to the port side. It then passes through the upright and the heeled equilibrium position where the kinetic energy of the roll motion
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A reviewof intact ship stability research and criteria 79
is at its maximum and ends with the utmost starboard heel angle where all the kinetic
energy is absorbed by restoring forces. If the righting lever at the final heel angle is positive
it will accelerate the motion towards the upright position.
Lever (a) Area (A+ C) >I Area (B+C) FIG. 5. Restoring lever Wind heeling
r lever
In this approach the following three parameters are of crucial importance:
The extreme roll anglesyiand q2.There is some disagreement over the selection of
cpi andcp,(Fig. 5b). The natural choice for cp2is the downflooding angle, because
beyond this
angle GZ curve does not exist. rPi is slightly more difficult because it isaffected by so many
factors. These were summarized by Cox (1977) as follows: (i) the zone of operation; (ii)
ratios GMIBand BIT; (iii) waterplane coefficient; (iv) midship form of the ship, i.e.whether
it is round or sharp bilged; (v) the extent and areas of the bar orbilge keels if fitted.
Empirical formulae for evaluating cpi are presented by Japanese Delegation (1979) and
U.S.S.R. Delegation (1979) but there is no evidence whatsoever on which is better.
Area ratio. In most conventional weather criteria some residual area underthe
righting arm curve is required to take care of all the possible dynamiceffects, which were
not included in the static moment calculations. This residual area is generally calculated
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-80 C. Kuo and Y. WELAYA
contains so many elusive factors not amenable to calculations. From the analysis of the data of 50 ships under the effect of 26 m/sec steady wind, Yamagate (1959) was able to conclude that an area ratio of 1.0 would be quite sufficient to protect from capsizing.
(c) Wind heeling moment. The evaluation of the wind heeling moment is a complicated
dynamic problem. Therefore, a simplified version that treats the dynamic problem by virtually static approach is currently used. In this case the wind heeling moment M,,, in the upright position is expressed by the formula
M =4 p,
D A H V2 (3) where pw is density of air; CO3 drag coefficient; A,, lateral projected area of vessel above operating waterline; H, wind moment arm between centre of lateral area and centre of underwater resistance; V,, wind velocity. There are various ways of using Equation (3) and in each case the parameters are given different values.In the conventional weather criteria it is always assumed, for simplicity, that the value of the wind lever is independent of the angle of heel cp. However, experiments indicate that the wind moment decreases as p increases. In the past it was customary to assume that it varies as Cos p or Cos2 p which virtually means that the ship has no breadth. For actual ships the wind does not reduce to zero at p equals 90° and according to some Japanese experiments (Kinoshita and Okada, 1957) Wendel (1960) recommended the
following formula to be used at different heeled positions:
Mw(9) = Mw(0) [0.25 ± 0.75 Cos3y]. (4)
The constant term shows that a percentage of the wind moment is still acting at heel of 90°. It is useful to consider the merits and demerits of this approach. Starting with the merits, the following points are worth noting:
Simple and realistic approach. It is a simple concept and certainly closer to reality because the analysis of the various heeling moments that may act upon the ship seems to provide a more suitable method for ensuring the safety of the ship (Nadeinski and Jens, 1968). In an attempt to replace this approach by a more realistic and sophisticated one, Amy et al. (1976) tried to solve the non-linear roll equation of a ship in irregular waves and a gusting wind, but they confessed that it was difficult to specify the use of non-linear time domain computer simulation studies of wind heel with rolling during the design of typical fishing and towing vessels and they recommended another criterion which is very similar to the weather criterion.
Suitable for new designs. It seems that this is the only way to ensure that new and unknown types of ships can be safe.
Flexible approach. It is a flexible approach which, apart from the wind effect, can include the other forces tending to heel the ship such as water trapped on deck, shift of cargo or passengers and high speed turning. This is, of course, a valid proposition only if the main assumptions of the approach are acceptable.
Suitable for various loading conditions. According to a Polish study presented to the
IMCO in 1978 (Polish Delegation, 1978) the weather criteria are more severe than the IMCO criteria especially in the light load condition. It would therefore appear that the
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adoption of weather criteria, as an interim solution, could improve the safety of vessels in loadings other than the fully loading condition.
(e) Evidence of success is available. There is evidence from the practical application that criteria based on this approach are successful. The U.S. Navy wind line criterion has been successful in providing adequate stability for U.S. naval vessels. There is also ample evidence that the U.S. wind heel and passenger heel criterion have been adequate for all
U.S. passenger ships built or operated in the last 50 years (Milleret al.,1975). The Russian,
Japanese and Polish experience leads to the same result.
However, this approach, like any other, has its own pitfalls. Some of them can be summarized as follows:
(a) The problem is over-simplified. As was pointed out by Bird and Odabasi (1975) the effect of wind and gust is not potential and steady. Therefore, this cannot be idealized in order to be introduced into the righting arm curve. The same criticism applies to the effect of water on deck because it certainly has a complicated dynamical influence. However, the static approximation with empirical constants to account for dynamic effects, is thought to be the only way which could realistically be expected to provide criteria in a form which
could be widely used (Amyet al., 1976).
The effect of waves is absent.The approach is completely dependent on the righting
arm curve in still water. It should, however, be remembered that the wind and gust moments
acting on the ship are not the only environmental effects. The effect of waves is absett and implicitly the approach assumes that the disturbing moment of wave is fully
com-pensated by the damping moment (Dorinet al., 1975).
The main parameters are arbitrarily selected. The results obtained depend on the values of the applied wind heeling moment and the initial angle of heel ch. It is highly
idealized and very arbitrary in the selection of these two important parameters (Amyetal.,
1976). This even makes it very difficult to compare national criteria in different countries. In spite of all the disadvantages of both approaches some people like Nickum (1978) are still of the opinion that the existing criteria with minor modifications will provide adequate stability.
6. DIRECTION OF FUTURE RESEARCH EFFORTS
-In 1975 during the -International Conference on Stability of Ships and Ocean Vehicles, Kuo and Gordon carried out a survey on the opinion of the delegates on the stability problem. Two questionnaires were given to the delegates on the first and last days of the conference with a view to identifying areas requiring further research studies as well as the
views on the present state of knowledge. There was a general agreement among delegates
that the followine areas of research were required as the most important in the order of priority:
Effects of waves on stability; Water trapped on deck;
Developing fresh methods to relate motion characteristics to intact stability; Gathering of full scale experience and feedback to design;
Conducting scaled model experiments; Wind effect;
(e) Education of ship masters and operators.
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It is now five years since that important conference and while there are likely to be
changes in the order of importance in all these topic areas, additional research is still needed. 7. CONCLUDING REMARKS
Having reviewed what has been done in the past, the following concluding remarks can 'be drawn:
Although the problem of intact ship stability has been under investigation for
over a hundred years no "final" solution has been reached. It isnot e:Tcp- ected that this stage
would be reached in the near future because of the complicated nature of the problem. Since a satisfactory solution based on the application of sophisticated theoretical methods would probably need many years to develop, the only practical way at the present is to try at improving the existing methods by taking into consideration as many key parameters as practicable.
Indiscriminate applications of the results of statistically analyzed casualty data would be unreliable. It seems that the only way this approach can be effectively used is when the developed criteria are employed to assess the stability of ships of the same type, size,
route and loading condition as those included in the sample. It is also essential for the
sample casualties to have been due to the loss of intact stability.
From the review of the existing criteria and their application, it is no longer valid to assume that one criterion will be sufficient to cover all stability needs. Stability criteria
must take into account the physical phenomena occurring during the ship'sservice.
It is obvious that the statical stability curve will continue to be important in any
further research. It is believed that when the GZ curves are constructed the effect of waves
on intact stability must be taken into account in a realistic and practical manner. The
effect of following and quarter seas on stability should beregarded as particularly important.
A survey on the future research direction indicated seven topic areas requiring
urgent attention.
AcknowledgementThe authors would like to acknowledge their gratitude to all participants in the Nine
Stability Workshops whose contributions to the discussions at Ross Priority, University of Strathclyde,
1977-79, were invaluable in the preparation of this Report.
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