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R.C.T.RAINEY*, J.M.T.THOMPSON**, G.W.TAM+ & P.G.NOBLE+
ABST RACT
Recent developments in the theory of nonlinear dynamics and chaos promise a
breakthrough in the description of ship "capsizability".They suggest that ship behaviour in transient conditions offers a highly repeatable index of "capsizability", which is quick and simple to establish by physical model tests or (in principle) comüEifsfrñiiTàtion. This index is the Transient Capsize Diagram. Using it ltou1d be possible, with the aid of suitable physical model tests and computer simulations, to resolve longstanding
arguments about the allowance which existing regulations should make for roll
damping, and for KG/draught ratio. Fpticularly critical vessels, where the cost of the model tests can bejusUfied, the Diagram itself ould be used
as the baili fitàbl]ity regulation, ands an operational aid. Looking
furthii ¡heact,roeñtevelopments in computer simulatf? vessel motions
may allow the Diagram to be calculated with satisfactory accuracy during the design stage, which would greatly enhance its practicability as a regulatory tool.1. 'THE CONCEPT OF THE TRANSIENT CAPSIZE DIAGRAN
The Transient Capsize Diagram, see Fig. i
below, was originally proposed in [1] and is conceptually very simple. It merely records the waveheight above which a boat will capsize, as a function of wave period,
and is determined by physical model tests or (in principle) computer simulation.
The novelty of the concept is entirely in the type of waves envisaged, which are groups of regular waves preceded by relatively calm conditions, so that the ship's roll notion is essentially
transient. This makes the physical model tests (or computer simulations) quick and simple to perform - the ship either capsizes during the transient, or it does not - so that it is practical to cover the extensive range of wave heights and periods necessary to complete the Diagram. By contrast, the existing practice of testing in irregular waves requires very long runs to obtain statistically significant
results, making it impractical to explore a
* Atkins Engineering Sciences Ltd.,
Woodcote Grove, Epsom, Surrey, UK ** Dept. of Civil Engineering, University
College London, UK
+ Wartsila Marine Inc., 1441 Creekside Dr. suite 570, Vancouver V6J 5S7, Canada
TNE U$ET
THE TRANSIENT CAPSIZE DIAGRAM - A ROUTE TO
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SOUNDLYBASED NEW STABILITY REGULATIONS
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Fa& U15 112C3comprehensive range of sea spectra (leaving aside the question of how such a
comprehensive range of spectra might be defined - the problem is that standard
families of sea spectra, e.g.
PiersonNoskowitz, generally have waves of
insufficient steepness)
More fundamentally, the novelty of the concept is in the argument behind the use of transient conditions, and the reasons why it should give results which are both repeatable (despite inevitable variations in the initial conditions of the boat at the start of the transient) and more searching th'an equivalent regular or irregular wave conditions. These reasons spring from an important breakthrough in dynamic systems theory, due to the second author and his associates, notably M.S. Soliman, at University College London.
This work is described in a series of papers [2] - [5], recently summarised in [6). The latest developments are given in the paper by M.S.Soliriian in these
proceedings. Essentially, it is shown that the extent of the "safe" initial conditions (i.e. the range of initial roll angles & roll velocities which do not lead to capsize in the transient conditions above) drops precipitously at a critical
waveheight. Moreover, this drop makes practically all small roll angles and velocities "unsafe", so the critical waveheight can be readily found by
examining transient motions starting from any such initial condition.
1 5%
10%
5%
WAVE STEEPNESS
STABLE
Fig. ''ow (taken from 14J)
illustrates a simple idealised case (roll alone, parabolic CZ curve plus harmonic excitation, with 5% critical linearised damping). It shows the area of the "safe basin" (i.e. the area
of noncapsizing
initial conditions in the 'phase space"of
roll angle y. roll ve1ocity), as a function of waveheight. The precipitous loss of basin area at a critical waveheight is evident. The small figures inset show the nature of the collapse in basin area - it is "from within", and covers the centre of the basin, corresponding to small initial roll angles and roll velocities.Also evident in Fig. 2 is the fact that the basin area does not vanish altogether until the waveheight is
increased by another 50% or so. This means that there remain a small range of initial conditions, corresponding to starting the
roll motion in a neartransientfree
Zero Heel
100 Heel
/
manncr, which will not lead to capsize. Thus model testing in long trains of
regular waves of slowlyincreasing height
will tend to
suppress capsizing, because it jsuppresses the transient. How mitch the
waveheight can be increased beyond the critical value
will
be ver\' sensitive to the extent of small disturbances during the test, SO the procedure (which has been widely adopted hitherto) will evidently give results which are bothnonconservative and erratic, compared with
t ransient test ing.
The final, and crucial, point is that the mechanism producing the sudden loss of basin area - chaotic transients from
incursive fractals - appears quite general. It should therefore occur with mathematical roll models roll of realistic complexity, as well as the simplified case considered above. Arid it should occur in physical model tests.
6 8
lo
I: 14 16 IS :0FiG. I TYPICAL TRANSIEJT CAPSIZE
DIAGRAM, FROM [1]
BEAM SEAS
QUARTERING SEAS
of SÌI IIASIN
.'i( 5) Il ll()t'Nt)ARV
2. USE OF THE TRANSIENT CAPSIZE DIAGRAM TO IMPROVE EXISTING STABILITY
REGULATIONS
2.1 Provision for KG/draught Ratio
It has been conjectured for many years that that a ship with a high KG/draught ratio will be more prone to capsize than one which has the same CZ curve, but a lower KG/draught ratio. Beamy shallow-draught ships, in other words, which justify a high CG by having an even higher metacentre, are widely suspected to be less safe than narrow deep-draught ships, which achieve the same CZ curve by means of a low CG.
One of the strongest pieces of evidence for this view is the case of the Danish coastal tanker "Edith Terkol", which capsized when sailing in a shallow-draught condition, in which its CZ curve certainly met the 1MO stability regulations, but in exactly the manner above (i.e. high CG but
higher metacentre). This capsize is highly significant in that it proved possible to
reproduce it repeatably in physical model tests [7].
Another piece of evidence is a more recent series of model tests commissioned by the US coastguard [8], which suggested that the existing 1MO stability regulations
SC CN A N I
r
I
ith
Jjfl, I;Ing,ncI R SII SI IJUIINI)AR',
(A167) are not valid for a KG/draught ratio above 1.4. More recent still is the capsize of the jack-up oil rig "Interocean 2' off Holland last year [9] - a jack-up rig under tow has an exceptionally high CG, offset by an exceptional beam and shallow draught.
Although the 1MO have discussed modifications to the existing 1MO
regulation (A167) to allow for high KG/draught ratio [10], the issue remains controversial. The latest 1MO proposal
[il], for example, calls for wind heeling-moment calculations, that would implicitly penalise some (but not all) cases of high KG/draught ratio.
lt is the purpose of this paper to
suggest that the Transient Capsize Diagram offers a means of ending the controversy, by demonstrating the increased
"capsizability" produced by high KG/draught ratio, in an unambiguous quantitative manner. Such Diagrams could clearly be constructed from physical models such as
the "Edith Terkol" - if moreover the same Diagrams could be produced by computer simulation (see 4.2 below), the physical mechanism responsible could be elucidated, so that a conclusive case could be
established for changing the existing regulations.
ii g iii
N'rniaiis,'i
HCIN( \i.\(;cr11l)i
J IFIG. 2
Provision for Roll Damping
Another longstanding and widelysupported
conjecture is that a high level of roll damping makes ships less prone to capsize.
Although the widelyadopted 1MO stability
regulations (A167) make no provision for roll damping, the latest 1MO proposal [11] requires calculation of the "overall area of bilge keels", which is certainly a
factor in roll damping.
Once again, however, no conclusive evidence is available of the extra safety margins involved, and the issue remains controversial. And once again, the purpose of this paper is to suggest that the
Transient Capsize Diagram offers a means of ending the controversy, by systematically demonstrating the quantitative importance of roll damping, in both model tests and computer simulations. These could then form the basis of logical modifications to the existing stability regulations.
3. DIRECT USE OF THE TRANSIENT CAPSIZE
DIAGRM AS A NEW REGULATORY TOOL
Existing stability regulations, of course, are merely an attempt to characterise the "capsizability" of a ship in terms of its stillwater righting lever (the CZ curve -in rare -instances, e.g. [12), the
rightinglever is also calculated by quasihydrostatic calculations in a
following sea).
The Transient Capsize Diagram is manifestly a much more direct measure of "capsizability", because it measures actual dynamic capsize behaviour in waves. It could be argued, therefore, that this Diagram should not be used merely as a means of justifying modifications to the existing stability rules, but itself as the basis of stability regulation.
/ This type of regulation would simply state that a ship must have a Transient Capsize Diagram of certain specified
minimum characteristics. This certainly has the attraction of simplicity and
incontrovertibility. For example, it would probably highlight the capsizability of the "Edith Terkol" compared with the "Gaul" (which could not be capsized intact during model tests [13]) - a verdict to which it would then be hard to refuse assent.
Moreover, the minimum characteristics required of the Transient Capsize Diagram could actually be calculated, on a
I semiscientific basis, by appealing to the desired Probability of Capsize, and the known statistics of ocean waves in the ship's operational theatre. This would
/ bring capsize safety into line with other
J
branches of marthe safety, wherequantitative risk analysis methodologies are followed.
Perhaps even more significantly, the dangerous combinations of ship speed and heading, and wave parameters, would be unambiguously highlighted; this would provide invaluable operational guidance, especially to inexperienced crews. The
"Edith Terkol", for example, might well have been saved if the dangerous following sea condition that capsized her had been displayed (on her bridge, say!) in a Transient Capsize Diagram.
The only objection to such stability regulations is cost. This is because they require a series of model tests to be performed, rather than a simple hydrostatic calculation. Especially at the design stage, when many alternative configurations may be under investigation, this is a considerable penalty. It could perhaps most
readily be borne in ships with a
particularly high value or long production run, and where payload is at a great
premium (e.g. warships or generalpurpose
trawlers, respectively).
For more general application, it appears necessary on economic grounds to consider the feasibility of calculating Transient Capsize Diagrams not by physical model tests, but by computer simulation. See 4.3 below.
4. THE RELEVANCE OF COMPUTER SI[ULATION 4.1 A New Credibility for Computer
Simulation, through Validation using the Transient Capsize Diagram
It is arguable that the major problem in computer simulations of ship capsize is no
longer in the computers or their programs, but in demonstrating that the simulations are giving a faithful description of
reality. For example, [14] describes one of the latest and most comprehensive
simulation studies, and displays several
hundred motion timehistories from
simulations and experiments, from which
it
is not at all clear how faithful the simulation is, in general terms, inreproducing capsize. This is because the
number of empirical parameters in the
program is large (so that oneoff agreement between theory and experiment can often be obtained by suitable choice of parameters), and the number of seastates under
consideration is even larger (and not all of them are relevant to capsize).
One of the purposes of this paper is to point out that the Transient Capsize Diagram appears to offer a major step forward in this area: by summarising in a single figure the capsizing behaviour of a ship over its whole operational envelope, it appears to be an ideal means of
displaying the veracity of a computer simulation, compared with a model test.
t =95
t =101
The problem of empiricallyset
parameters within the computer program, in particular, can be 'brought into the open" by recomputing the complete Diagram (a task
clearly wellsuited to a computer graphics
package linked to the simulation outputs) for a suitable range of all the relevant parameters.
It is perhaps therefore mt fanciful to suggest that computer simulation of vessel capsize will in the next ten years gain considerable credibility, by this essentially pictorial means. And that there is an analogy with the theory of nonlinear dynamics and chaos, which has gained
considerable credibility in the last ten
years, through similar computergenerated
pictures (see e.g. [15J)
4.2 Computer Simulation as a Means of Elucidating the Physical Mechanisms of Capsize
Having established the validity of the computer simulation, an extremely important use to which it can be put is to elucidate the physical mechanisms involved in
capsize. This is possible because a
t =97
103 sec
FIG. 3 "FROUDEKRILOVTYPE" COMPUTER
SIMULATION OF FISHING BOAT CAPSIZF, FROM
computer simulation inevitably incorporates some idealisations and simplifications of the ship dynamics, which break down the forces acting into
comprehensible elements. These individual forces can thus be
displayed at each timestep, so that the critical ones can be identified.
For example, it should prove possible to identify in this way the physical mechanism linking the large KG/draught
ratio of the "Edith Terkol" to its
propensity to capsize. lt has already been demonstrated [71 that the variation in
quasistatic GM in various wave positions
(i.e. variations calculated in the manner of [12]) are irrelevant. It is possible, however, that the heaving motion of the ship produced changes in instantaneous displacement which gave large GM
variations, or that lateral hydrodynamic drag forces were to blame, as speculated in
[71.
The truth or otherwise of all these explanations can be readily
explored with a reist ively simple
"FroudeKriiovtype"
computer simulation, such as that used in [16]. Fig. 3 above illustrates computer graphics from [16]
d (AQWANAUT from WS Atkins) simply integrates the water pressure in an undisturbed wave over the instantaneous wetted surface of the hull, combines it with an approximation to the hydrodynamic effects, and solves the ship's rigidbody equation of motion.
However it is accomplished,
the goal of finding the physical mechanism
responsible for a capsize is undoubtedly worthwhile in practical
terms. It is the "smoking gun" which, if submitted in
addition to the modeltest
evidence, alone appears capable of achieving
change at the international, or even national, level. 4.3 Computer Simulations as a
Regulatory Tool in their Own Right
The ultimate goal for computer simulation is to provide a direct replacement
for physical model testing,
thereby offering the speed and flexibility in calculation
of
Transient Capsize Diagrams, which alone makes them an economic
generalpurpose
replacement for stability
regulations in the present style.
This is however a much more
challenging goal than merely identifying the main physical
mechanisms involved in a
particular capsize, as above. The reason is that the computer
simulation is required to
be generalpurpose - for example correctly
modelling all three of the canonical capsize mechanisms
originally highlighted in [17], viz. "pure loss of stability
in waves", "low cycle resonance" and
'broaching", to which might perhaps be added "resonant rolling in beam seas" (as primarily envisaged in [1J - [6]). And the hydrodynamic mechanisms involved are
very different - the first two being widely
supposed to be largely
quasihydrostatic
problems, the third a matter of directional stability (which involves keel & rudder design, etc.), and the last a matter
of roll damping among other things.
For a semisubmersible
oil rig, the hydrostatic and hydrodynamic phenomena
are greatly simplified
because the effect of the free surface
is relatively slight, and because the structural members can be treated as slender bodies. A rigorous
slenderbody approach [18] therefore looks promising for generalpurpose applications, as argued in [19]. It is possible that a modification to this approach [20] will prove satisfactory for ships too: at least the rigorous
methodology of [18] has the advantage that the
final equations of motion are based on a consistent
approximation scheme, and therefore lead to computer programs which can be debugged by comparisons with
classical analytical solutions. This is in contrast to the
semiempirical approach of [14], in which
a
large number of separate and essentially arbitrary approximations are made, making the program
very difficult to debug.
In any event, the
challenge is clear
-the feasibility of finding Transient Capsize Diagrams by computer simulation will only eventually
be decided by trying it in practice.
5. CONCLUSIONS By describing a ship's capsizing
characteristics in waves over its whole operational envelope, the Transient Capsize Diagram appears capable of bringing a
muchneeded focus to stability research.
In particular, it should:
Clearly establish the capsize risks inherent in high KG/draught
ratio and low roll damping.
Thereby give useful operational guidance on problem
vessels, and pave the way for rational
improvements in
existingstyle stability criteria
Provide a format for
establishing the validity of computer
simulations, enabling them to be used to discover the physical mechanisms
responsible for capsize
Ultimately establish the validity of computer simulations sufficiently for them to be used directly as a means of "scientific" stability regulation. RE FE RE N CES
RAINEY, R.C.T. & THOMPSON, J.M.T. The Transient Capsize Diagram - a new method of quantifying stability in waves, J. Ship
Res. 199e in press
THOMPSON, J.M.T. Chaotic phenomena triggering the escape from a potential well, Proc. R. Soc. Lond. A421, 1989,
pp
19 5-225
SOLIMAN, M.S. & THOMPSON, J.M.T.
Integrity measures quantifying the erosion of smooth and fractal basins of attraction, J. Sound & Vibration
135(3), 1989, pp
45 3-4 75
THOMPSON, J.M.T. & UEDA, Y. Basin boundary metamorphoses in the canonical escape equatian, Dynamics
& Stability of Systems 4, 1989, nos 3 & 4
THOMPSON, J.M.T. & SOLIMÁN, M.S. Fractal control boundaries
of driven oscillators and their relevance
to safe engineering design, Proc. R. Soc. Lond. A428,
1990, pp 1-13
THOMPSON, J.M.T.,
RAINEY, R.C.T. & SOLIMÁN, M.S.
Stability criteria based on chaotic transients from incursive
fractals, Phil. Trans. R. Soc. Lond. A332,
7. lUiRE, K. &
BANG, C.J. The
ultimate half
roll, Proc. mt.
Conf. on Stability of Ships and Ocean
Vehicles London: Dept. of Trade & Industry,
1975
NICKUÌI, G.C., An
Evaluation of Intact Stability Criteria Marine Technology
Vol. 15, 1978 pp 259-265
INTEROGEAN 2 sinks
in North Sea North Sea Newsletter,
November 11 1989 JENS, J.L.E. &
KOBYLINSKI, L., 1MO activities in respect of international requirements for the stability of ships Proc. 2nd lot. Conf, on Stability
of Ships & Ocean Vehicles
Tokyo: Soc. Nay. Arch. Japan, 1982
1MO recommendations
on a severe wind and rolling
crtierion (weather criterion) for the intact
stability of passenger and cargo ships of 24m
in length and over 1MO intact stability
criteria for passenger cargo ships 1987 ed
London: International Maritime Organisation,
publication No. 832
87. 13.E
ARNDT, B., BRANDL, H. & VOGT, K., Froc. 2nd Int. Conf.
on Stability of Ships & Ocean Vehicles
Tokyo: Soc. Nay. Arch. Japan, 1982
MORRALL, A. The Gaul disaster: an investigation into the loss of a large stern trawler Trans.
R. Inst. Nay. Arch. 123, 1981, pp 391-440
DE KAT, J.O. & PAULLING, J.R. The simulation of ship
motions and capsizing in severe seas Trans. Soc. Nay. Arch.
& Marine Engrs. 1989, paper read to annual
meeting. THOMPSON, J.M.T. & STEWART, H.B.
Nonlinear dynamics and chaos Chichester:
Wiley, 1986
MILLER, D.R., TAM, G., RAINE?,
R.C.T., & RITCH, R.
Investigation of the use of modern ship motion
prediction models in identifying ships with a larger than acceptable risk of dynamic capsize, Transport Canada, report TP7407E
FAULLING, J.R.,
OAKLEY, 0.H. & WOOD, P.O. Ship
capsizing in heavy seas: the correlation of theory
and experiments Proc.
mt. Conf, on
Stability of Ships and Ocean Vehicles London: Dept. of Trade &
Industry, 1975
RAINEY, R.C.T. A new equation for calculating wave loads on offshore structures J.Fluid Mech. 204, 1989
pp 295-324
RAINE?, R.C.T. A new theory and its application for stability criteria covering
waveinduced tilt phenomena on
semisubmersibles, Proc. mt. Conf. Stationing and Stability of
Semisubmersibles London: Graham & Trotman, 1986, pp 41-59
20. RAINE?, R.C.T. Energy
arguments under a "wavy lid' - a new approach
to capsizing and other highly
nonlinear phenomena Proc.
5th mt. Workshop
on Water Waves and Floating Bodies
Manchester University: Dept. of Mathematics 1990
