Abstract    In this paper the intact stability of small container ves-sels is investigated, both in calm water and in a seaway.  The research was triggered by the capsizing of the con-tainer feeder ‘Dongedijk’ near Port Said in August 2000. It is shown that a combination of over-loading, a ‘flat’ part in the righting lever curve and a large trim to the stern can cause an accumulation of water on deck due to heel when changing course, which results in an extreme heeling angle and finally capsizing of the ship.  58496
The stability sensitivity for cargo weight and position together with the occurrence of the above-mentioned static undefined regions within the stability curve is further being looked at. A static study is performed for two vessel designs: one with a minimal freeboard and one with a higher freeboard but with the same hull shape and deadweight capacity.  As it was suspected that a low-freeboard vessel with similar stability characteristics could be susceptible to instability in a seaway, non-linear numerical simulations were performed in order to determine the probability of capsizing for various wave conditions. For the calcula-tion of these probabilities  the program FREDYN was used. In order to validate the FREDYN calculations for this ship type and to collect more data about the abso-lute risk values, model tests have been performed. The results of the model tests and the calculations in a sea-way are compared and discussed.  The findings of this study contribute to the safety at sea in two ways. - Information about the stability sensitivity of a ship is of importance for crews when operating this kind of ships as well as for the designers when optimising a design. - The results from the simulations in seaways can contribute to the possible revising of cur-rent stability criteria values on the short term and provide information for a new set of rules on the long term.   Keywords Stability; risk analysis; model tests; container vessel.  Introduction The past ten years of container feeder development statistics show a decline in the average Gross Tonnage (GT) per container carried. This decline is the result of attempts to reduce the harbour and channel dues, which are often related to the GT value. With container vessels (especially feeders), lowering the GT is mainly achieved by increasing the amount of deck cargo and reducing the design freeboard to the minimum legal limit.  In this study the link between this low freeboard and the intact stability is investigated, both in calm water and in a seaway.  The research was triggered by the capsizing of the con-tainer feeder ‘Dongedijk’ near Port Said in August 2000. The accident occurred in calm water.    According to the Dutch Shipping Counsel (in Dutch ‘Raad voor de Scheepvaart’, see [1]) the main contribut-ing factor was the overloading of some 150 tons above the maximum design deadweight. Thirty percent of the containers taken on board turned out to be more than one ton heavier than was stated on the bill of lading, causing the total container weight to be 178 tons more than the weight figure communicated by the shipping agency. Together with the large trim aft of 1.6 metres, the freeboard just in front of the rear bulwark was re-duced to only 0.7 metres. The design freeboard of this vessel is 1.3 metres.  This low freeboard reduces the angle at which the deck edge submerges. The loading condition the ship had during the capsizing reduced the angle to around five degrees, above water will be forced onto the deck, due to the forward speed of the vessel. When this water is trapped, it will cause a heeling moment. Whether this heeling moment will lead to the capsizing of the vessel  depends on several factors like: initial stability, speed, intake and discharge area. Although the capsizing of the “Dongedijk” was primar-ily caused by problems with the loading of the ship and the failure to detect those problems, the accident has a deeper background, which could affect (or jeopardize) more ships of the feeder type. In order to identify the possible dangers, it was considered relevant to investi-gate the accident with the “Dongedijk” further.    Capsize in calm water  The stability curve of this ship with a large B/T value and a small freeboard shows a static undetermined re-gion between the heeling angles of 12 and 20 degrees (see Figure 1). This part of the curve plays an important role where static load cases are involved (of which the collection of water on deck  is one). When the angle of 12 degrees is reached, the ship will suddenly heel to the next stable angle of 20 degrees, or even more due to dynamic effects. At this angle part of the hatches will be submerged as well as several ventilation openings. If this heeled con-dition is sustained for some time, water will enter the hold and other compartments. The ship will heel further and finally capsize.    last voya ge-0,1-0,0500,050,10,150,20,250,30 5 10 15 20 25 30 35hee ling angle (deg)GZ(m)GM=0, 772 mc ri t ic al hee l in g angl e12 52028,5critical heeling arm0,104 m  Fig 1: Righting lever curve “Dongedijk” last voyage  To determine if water on deck is a possible contribution to the capsize event, we need to look at the possibility of heeling angles being created  larger than the angle at which the deck edge submerges (in this case five de-grees), and if so, is it possible to collect enough water?   Heeling angle due to a change in course  Because the capsizing happened just after a change in course, it is interesting to determine the heeling angle that could be expected when applying rudder. The maximum heeling angles were calculated using the MARIN program SurSim, which calculates the hydro-dynamic reaction forces on a ship in the horizontal plane in order to simulate the manoeuvring behaviour of  the vessel.   The simulations were performed for a whole range of speeds, metacentric heights and rudder angles. If we take the conditions as they were during the capsizing, a speed of 11 knots, a GM-value of around 0.77 metres and the maximum rudder angle set to 10 degrees, a maximum heeling angle of 6 degrees could be expected (see Figure 2). This value is conservative, because above 5 degrees the stability curve shows a non-linearity that is not taken into account by SurSim.     critical area10 deg rudder angle ('Barke' rudder)02468101214160.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8GM (m)speed (kn)critical angle: 5 degcritical angle: 10 deg UNSAFEUNSAFESAFE Fig 2: Expected heeling angle when turning  Even when the wave pattern, created by the hull, is taken into account (influences on the effective freeboard by way of the actual wave pattern, squat and change in trim) the expected angle due to a change in course is still larger than the angle at which the deck edge will submerge. With dynamic influence taken into account this angle increases to 5.5 degrees. This means that water will be forced on deck under these circumstances.  The collection of water on deck Although the coaming does run all the way to the poop, the aft part of the deck is exposed. There are no hatch covers fitted, since the containers are on the deck above the engine room. The coaming is therefore provided with freeing ports which will allow water to reach the deck in front of the poop. The containers are placed on twist-locks, which leave a gap of around 10 centimetres between the deck and the bottom of the containers.   The distance between the coaming and the aft bulwark is about one metre. This opening works as an intake area when that part of the deck is submerged. At speed (the speed of the ship at the time of capsize was 11 knots), water will be forced though the gap onto the deck.  In order to be able to make an estimate about the speed and the amount of water needed to cause a heel larger than the critical angle of 12 degrees, a computer model called ‘Water flow’ was created by the Delft University of Technology.  The model is based on the relation between the amount of inflowing water on the deck in front of the poop and the heeling angle.   The ‘Water flow’ simulation does a trend, which sug-gest an exponential decrease  of time needed with an increase of initial heeling angle.  Furthermore the calculations show that it is possible to collect a sufficient amount of water on deck to increase the heeling angle to 12 degrees (the angle where the static undetermined region starts). In total 40 m3 of water on deck is sufficient to cause the vessel to heel to 20 degrees. Due to the flatness of the stability curve between 12 and 20 degrees the dynamic angle can be more than 20 degrees.  Model tests (part of the test in waves as described be-low) confirm an accumulation of water on deck (see Fig 3). The model tests show occurrence of capsize at 13 knots, even with small rudder angles. At slightly lower speeds the vessel heels dangerously.     Fig 3: Model in calm water turn just before  capsize   Stability sensitivity The investigation into the accident also brought a sensi-tivity of the intact stability on changes in deadweight and centre of gravity position to light. This sensitivity was further investigated by comparing the stability changes with a reference vessel, called the “Delft Feeder”.  The freeboard of this reference ship was increased from 1.3 metres to 4.0 metres, i.e. one additional layer of containers below deck. The hull form remained the same as the low freeboard version in order to exclude any influence of the change  in hull shape on the stabil-ity. The total number of container positions is somewhat lower than in case of the low freeboard vessel, but the same actual loading conditions can be achieved.  The righting lever curves of the two vessels show a clear difference (see Fig 4). The occurrence of a static undetermined region (even with approved loading con-ditions) for the low freeboard  feeder is, together with the large difference in dynamic stability, one of the most obvious differences.  Righting leversdesign condition -0.20-0.100.000.100.200.300.400.500.600.700.800.901.000 5 10 15 20 25 30 35 40 45 50 55 60 65 70heeling angle (degrees)righting lever (m)high freeboard feederlow freeboard feederdwt = 3696 tonVCG = 6,35 mGM = 0,68 m  Fig 4: Righting lever comparison  This large difference can also be seen when the dead-weight is increased. In general, the values for the IMO stability criteria (in Fig. 5 the area-criteria are given) for the low freeboard feeder reduce 2 to 2.5 times as fast as for the high freeboard feeder. This means that when irregularities occur with the load-ing of the vessel, the already marginal stability of the low freeboard feeder will also reduce faster.    Dwt variationArea criteria-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.103600 3700 3800 3900 4000 4100dwt (ton)dArea / AreaminArea 0-30 lowArea 0-30 highArea 0-40 lowArea 0-40 highArea 30-40 lowArea 30-40 high  Fig 5: Dwt sensitivity comparison  For changes of the vertical centre of gravity position, the difference concentrates on the angle of maximum righting lever and the change in value of that righting lever. The dynamic stability reduces for both vessels equally fast with a GM decrease.   Because variations in the vertical position of the centre of gravity are hard to detect, is it of paramount impor-tance that deviations in cargo weight are carefully as-sessed and the stability checked on all applicable stabil-ity criteria.   Ship Behaviour in Waves  In order to establish a capsize risk assessment for opera-tional sailing conditions, seakeeping model tests were carried out in the Seakeeping and Manoeuvring Basin of the Maritime Research Institute Netherlands (MARIN). The model tests aimed at establishing the conditions were capsizes could be observed.   Because only a limited set of data is available, the model test data can not directly be used to establish the capsize risk for every loading condition. Instead they demonstrate the existence of this risk when sailing into mation to validate the seakeeping program FREDYN that will be used to perform the final risk assessment in the latest phase of the investigation.  The model A wooden ship model was manufactured at a scale 1/25, see Fig 6.     Fig 6: Small container feeder model  The ship was self-propelled  and steered with an auto-pilot. Bilge keels and a flap rudder were fitted.   Three loading conditions were tested (GM = 0.68 m, GM = 0.73 m, GM = 1.03 m) the draft and radii of gyra-tion were unaltered and represent a fully loaded design case.   The deck arrangement (see Fig. 7) was carefully repre-sented to allow water to flow as on the real ship. How-ever, the containers were not modeled. Despite that in reality, the containers protect a large part of the deck from being flooded and hence potentially represent some additional reserve of buoyancy, the choice was made not to include the cargo on the ship model. The main reason not to model the containers is the that the safety of the ship should not depend on its cargo. In addition, containers are not watertight. Successive wash of the containers might yield some containers to trap water, creating then a possible free surface effect and extra weight that would reduce the ship stability over the time. As such a complex modeling is not possible, the choice not to represent the container was adopted.    Fig 7: Deck arrangement on the model  Test Methodology The tests were carried out at an average sailing speed of 13 knots in irregular waves. For each test condition, order to gather sufficient wave oscillations.   Most of the tests occurred in stern quartering seas as this condition gives the highest risk of capsize according preliminary calculations.  For each condition, a minimum of 4 runs (1 wave cycle of 30 minutes) were carried out. When no capsize was observed after the 4 runs, then the significant wave height was increased by 1 m and the runs were repeated. The wave height was increased until a capsize was ob-served or until the wave steepness was too high to rep-resent realistic sailing conditions.  The initial methodology was meant to investigate 3 more wave cycles when a capsize was observed. Hence, an approximation of the probability of capsize over 30 minutes would have been obtained within two hours of testing.  Due to time constraints in the basin, this methodology was applied for a few tests only. For most of the tests, the test duration was between 30 minutes to one hour.   Conditions with capsize Four main irregular waves with different peak periods were investigated. The wave heights yielding the ship to capsize are summarized in the Table 1:  Table 1: Test conditions GM (m) 0.68 0.73 1.03  Heading (deg) Tp(s) 330 315 330 315 315 9.64 N.C. 9m (*) Not tested N.C. 9m 10.5 7m (*) 9m 9 m N.C. 9m Not tested 13.5 7m (*) 8m  Not tested N.C. 11m 14.7 9m  Not tested       The “N.C.” label means that no capsize was observed while increasing the wave height up to the indicated wave height.   (*)  for these tests the results are based on a sailing duration of 2 hours (4 wave cycles). They are only based on a maximum of 30 minutes otherwise.  The table shows that with  the lowest GM, a significant wave height of 7 m represents a potential danger. This also means that with Hs = 6m, the ship did not capsize after two hours of sailing duration. However it does not necessarily imply that Hs = 6m is a safe sailing condi-tion.   Fig 8:  Ship model capsized  Increasing the GM has a strong effect to the safety as only one condition yielded a capsize in a very large sea state (Hs  = 9 m) with an increase of GM of only 5 cm.  The test also showed that if an average heel of 10 de-grees is given to the model, the limiting wave height decreases by one meter. This heel could be attributed to the wind forces and/or an asymmetry of the loading condition due to the loss of one or more container.  The behavior of the ship at the time of a capsize suggest that the capsize is due to loss of stability. See also Figs. 8 and 9.    Fig 9: Ship model losing stability on a wave crest.                               Toward a capsize risk assessment The results of the model test show that the ship faces a real risk to capsize when  it is in operation. However these results do not provide regulation authorities with sufficient information to directly derive a modification of the regulation as the optimum balance between the cost and the safety of the ship.   Although an increase of GM is obviously a beneficial solution, the GM value that could be set as a limit by the regulation can not yet be obtained.   The solution requires computer simulations which re-produce the behavior of the model in the basin and which can be used on a large number of sailing condi-tions and for a wide range of loading conditions. In this way, the capsize risk could be established as, for in-stance, a function of the GM value.    Model tests versus calculations  Calculations were performed with the seakeeping pro-gram FREDYN [2]. Originally developed for the Coop-erative Research Navies, FREDYN is a time domain seakeeping and manoeuvering non-linear program which makes use of a large set of empirical manoeuver-ing coefficients that were originally derived for frigates. The seakeeping part of the program accounts for the instantaneous Froude-Krylov forces up to the ship deck while diffraction and radiation forces are transferred to the time domain from the frequency domain by means of retardation functions.     In order to use this program to establish a final risk assessment, a sufficient agreement between the model tests and the prediction of the calculations must be ob-served.  Roll Damping The most convenient way to check the accuracy of the roll damping model is to simulate a roll decay test to compare it the one obtained in the basin. As shown if Fig 10 this comparison is satisfactory and provides a good level of confidence in the roll damping model used by FREDYN.   Ship speed = 13 knots-4-3-2-1012345020406080100Time (s)Roll angle (deg)FREDYNModel Test Fig 10: Comparison of roll decay test at 13 kn  Roll motion in small regular wave The roll motion is the most difficult quantity to predict as it is influenced by several sources of non-linearities. These non-linearities are related with: the non-linearity of the restoring moment, the non-linearity of the roll damping (the roll damping coefficient increases with the roll amplitude) and the non-linearities of the wave forces when water floods on the ship deck. Another source of non-linearity is the coupling between the ma-noeuvering model and the seakeeping model. For in-stance, the rudder might reach its limiting angle or the speed variations due to surf ridding can yield the en-countered waves to be slightly different when the wave height is increased.  Most of these non-linearities will become significant in high waves. In low waves, only the non-linearity of the roll damping should have an influence. It is then of interest to know if in modest wave conditions FREDYN provides a satisfactory prediction. This is shown in Figure 11 where FREDYN and the model tests are compared for regular waves with 1 m amplitude. The correlation between FREDYN and the model tests is in this case very satisfactory.   Fig 11: Roll amplitude (deg) as a function of wave fre-quency (rad/s) in regular waves of 1m   This comparison, together with the decay tests, shows that when only few non-linearities are involved the agreement between FREDYN and the model test is very high.    Roll motion in irregular waves Our main interest lies in the prediction of the behavior in conditions that can yield the ship to capsize. Hence, the prediction of the roll motion in irregular waves with high amplitudes is the most important.  There are two major difficulties to compare the behavior in irregular waves:  First, it is not yet possible to perform a deterministic comparison where the simulation would reproduce the exact wave train in which the model sailed during the experiments. The only way to compare the tests in ir-regular waves makes use of the statistical proprieties of the roll motion.   The second difficulty is that the statistical proprieties can only be accounted for when sufficient oscillations have been gathered (from both sources of data: the model test and the simulation program).  Unfortunately, only very few tests were long enough to provide relevant statistical information. As the tests occurred in stern quartering seas with a significant for-ward speed, a sailing duration of 30 minutes provides only around 100 oscillations.  The Figures 12 and 13 illustrate the measured and cal-culated cumulative distribution of the roll amplitudes. This type of graph shows the probability of exceedance (vertical scale) of a roll angle (horizontal scale) from both sources. If we compare Figures 8 and 9, we see that increasing the wave height decreases the agreement. 小型集装箱船的安全评估英文文献和中文翻译:http://www.751com.cn/fanyi/lunwen_63424.html