On Safety of Inland Container Vessels Designed for Different Waterways

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2 Nη( η) = nη η + ρascs η η Nϕ( ϕ) = nϕ +µ ϕ +β ϕ ϕ ( ) Nϕη = nϕη η ρasc sls η η. In the present investigation following [3] all added masses m η m φ m ηφ = m φη and potential damping coefficients n η n φ n ηφ = n φη are obtained by the use of classical strip-theory technique. Linear and nonlinear parts of viscous roll damping µ β are obtained by Ikeda method (see [4]). The coefficient of nonlinear sway damping force is taken approximately as a constant c S.. The last (restoring) term on the left hand side of the second (roll) equation is righting moment [ ] Mst ( ϕ) = gd h ( ϕ) = gd h ( ϕ) + MG sinϕ where the additional moment lever is approximated for each tested vessel by an odd polynomial of the form N an+ n= 0 n h ( ϕ) ϕ +. The first terms on the right hand side of the () present side wind force and moment Fw = ρwawc w vw M w = ρwawc wlw vw where apparent wind speed (wind speed relative to vessel) is () vw t = vw + vw η. Absolute mean wind speed v w is taken from the present stability rules (e.g. v w = 8 m/s for zone ) while v w presents the gusting wind speed N vw t = An nt+αn n=. () cos( ω ) The amplitudes of gusting wind speed is obtained from wind spectrum n ( ω ) A = S dω where as in the previous investigation well known Davenport spectrum is used w S( ω) = 4K v X ω D 4 3 ( + X D ) n X D 600ω =. π v The last terms on the right hand side of () are (somewhat) artificial. They present side force and moment Fr = ρ Asc sv M r = ρ Asc slsv w added to the equations to keep the vessel exposed to the side wind on her course. Namely as explained in [3] the beam wind tends to drift the vessel out of her course by constant drift speed k v v k v + k η = w w ρa cwaw k =. ρ c A However in realistic circumstances vessel s master would not allow that so would try to keep the vessel on course by the use of the rudder. To simulate (approximately) such course-keeping model a constant force F r and (an appropriate moment M r ) have to be embedded to equations of motion where (as found by numerical experiments in [3]) the speed v should be taken a few percent larger than the free drift speed v η. With all the coefficients for the particular vessel found the system of equations of motion is solved numerically by Runge-Kutta method and vessel roll and sway motion φ(t) η(t) obtained. By the statistical analysis of the roll time history (see e.g. []) the mean angle of roll ϕ and standard deviation s φ due to beam gusting wind are found. The probability that the vessel would heel to some prescribed angle φ is then: φ ϕ P = exp Nc exp s ϕ φ ϕ Nc exp. s ϕ This result enables the risk-based analysis of the ship safety in the beam storms. It makes possible to analyze by numerical experiments the risk of flooding capsize etc. and to obtain its dependence on various vessel and environmental characteristics. As announced in the Introduction it would be used here to find the correlation of the probability P to the vessel design draught. 3. SAMPLE VESSELS Investigation was conducted on typical European inland container vessels 0 m long and.4 m in beam designed to carry TEU containers in 3 bays and 4 rows Fig.. It was supposed that all the vessels are loaded with 5 container tiers which is the very maximum that could be achieved with a careful vertical load distribution only (see [5]). The vessel draughts vary from. m up to 3. m. The minimal value is suitable for the transportation on the lower Danube while the maximal value is suitable for the Rhine so the vessels with those extreme values of draught would be termed (for the sake of clarity) the Danube Vessel and the Rhine Vessel respectively. All the vessels have open cargo holds with no hatch covers and the minimal freeboard of 0.6 m as prescribed for instance by UNECE Regulations for open hold vessels operating in zone (see [6]). It is supposed however that the vessel hatch coaming height can vary between the minimal s s 5 VOL. 36 No 008 FME Transactions

3 value of 0.4 m (indirectly prescribed by the Rules [6]) and some (technically reasonable) maximum of.5 m. The changes in the hatch coaming height directly influence the flooding angle and therefore significantly impact the vessel safety. Figure. A typical European inland container vessel Additional righting moment lever h'(φ) for the Danube and the Rhine Vessel are presented in Figure. All the other vessels tested have their righting levers between these two extreme curves. In the calculations of roll damping it was supposed that all the vessels sail with service speed of 6 km/h. Figure. Additional stability levers of sample vessels The following fact concerning the assumed container loading should be stressed. If the vessels with fully utilized cargo space (number of TEUs fixed to maximal) and full cargo-weight capacities differ in draught they would also differ in their displacement and the average mass of containers. The dependence of the average container mass on the draught can be found (see Fig. 3 taken from [5]) showing that the fully loaded container vessels designed for shallow waterways would be able to carry very light containers only. It is believed that the series of standard 0 m.4 m vessels selected for the numerical tests does represent the most suitable choice for the analysis of the influence of varying draught on the vessel safety. Figure 3. Average mass of container as a function of vessel draught (calculated for typical fully loaded container vessel L = 0 m B =.4 m 5 tiers of containers [5]) 4. NUMERICAL TESTS The outlined procedure was used to calculate the probability that the vessel s open container hold would be flooded in two hours under the action of gusting beam wind. The mean wind speed was supposed 8 m/s as prescribed by most of inland stability rules for the vessels operating in zone. The terrene roughness was assumed 0.05 suitable for suburban areas. The permissible probability of flooding in the beam storm was accepted P a = O(0-3 ) as discussed in detail in previous papers []. The obtained probabilities of flooding depend on three parameters: designed draught hatch coaming height and metacentric height. The design draught and hatch coaming height are the characteristics of the vessel while the metacentric height depends on the loading conditions (or more precisely on vertical position of centre of gravity). The results are as in all previous investigations presented and analyzed in the convenient form of (so called) probability curves P = f(mg). The probability curves for the Danube and the Rhine Vessels for different hatch coaming heights are presented in Figure 4. The region of unacceptable probabilities (too high risk of flooding) is shaded. As indicated earlier the results show that the vessel of smaller draught would have higher risk of cargo hold flooding. More precisely if H c (Danube Vessel) = H c (Rhine Vessel) MG (Danube Vessel) = MG (Rhine Vessel) follows that P (Danube Vessel) > P (Rhine Vessel). This is generally valid for any hatch coaming height. The quantitative difference of probabilistic results varies with metacentric height and hatch coaming height and becomes in some cases substantial. For example if H c = 0.4 m and MG =.4 m the probability of flooding of the Danube vessel is O(0 - ) which is considered as unacceptably high risk. The corresponding probability of the Rhine vessel is O(0-4 ) indicated that these vessels under the same conditions are safe enough. The impact of the design draught presented in Figure 4 could be expressed in a different way also: inland vessels designed for operation in shallower waterway (the Danube) would obtain the same level of safety in beam storms as the vessels for deeper waterway (the Rhine) if their metacentric height is increased for some 0 30 cm. The obtained result showing that the container vessels of smaller draught are more vulnerable to the beam wind could be physically explained. Namely if the number of containers is fixed to maximal the change of draught impacts the area exposed to wind wind moment lever and the vessel displacement. The results indicate that the prevailing effect is the change of displacement and consequently the change of vessel righting moment. The decreased draughts reduces the displacement implying considerably smaller righting moment with insignificant changes of exciting wind moment only. FME Transactions VOL. 36 No

4 4. Probabilistic analysis of stability regulations Figure 4. Probability curves of the sample vessels for different hatch coaming heights The vulnerability of the vessels with smaller draughts demonstrated in Figure 4 could have been (perhaps) assessed intuitively. The main question is however how the present stability regulations comply with that phenomenon. Are the rules for the shallow-draughted vessels stricter so that the vessels of different draughts complying with minimal stability requirements of the rules would have the same risk of accidents? In should be repeated that in the previous investigation [-3] the inland container vessel stability regulations were found insufficient. It was demonstrated that these vessels complying with the minimal stability requirements (minimal metacentric height minimal freeboard and safety distance) could have unacceptably high risks of flooding. However these investigations were carried out on vessels of.6 m draught (suitable e.g. for the middle Danube). How do the obtained disturbing aspects of present regulations apply to the vessels of higher and lower draughts? As in [] and [3] UNESCE Stability Rules [6] would be used as a typical representative of the present inland safety regulations. According to these rules inland container vessel needs to fulfill some additional stability requirements besides basic ones that apply to all inland vessels. A container vessel should comply either with criteria of Method A (which is the same as stability criterion of ADN Rules [7]) or with those of Method B. Some of the principal features of Methods A and B will be just briefly accounted here while the more extensive critical analysis of the Rules is given in []. Both methods A and B distinguish vessels carrying fixed and non-fixed containers. Both methods explicitly prescribe m as minimal metacentric height for a vessel intended to carry non-fixed containers. In the case of fixed containers however the methods split: Method A sets 0.5 m as the minimal metacentric height while Method B makes no similar explicit restraint so the minimal metacentric height follows from the other rule demands (i.e. inland weather criterion static wind-heel criterion see []). The minimal metacentric height as function of vessel draught calculated according to UNESCE Rules Method A and B for vessels carrying fixed and non-fixed containers is presented in Figure 5. The other requirements of the Rules affecting stability of vessels include the minimal freeboard and (so called) minimal safety distance implying that the open cargo hold vessels operating in zone should fulfill the following conditions: Minimal freeboard (F B ) > 0.6 m Minimal safety distance (F B + H c ) > m. As for all the vessels tested the freeboard is fixed to its minimal value this requirement implicitly determines the minimal hatch coaming height as (min) H c = 0.4 m. It follows in all the examined cases that only the metacentric height for fixed containers Method A is dependant on the vessel draught. All the other requirements are the same for all the vessels tested regardless of their draught. 54 VOL. 36 No 008 FME Transactions

5 hatch coamings in spite of the fact that the Rules allow them. To reach the proper probabilities of flooding the vessels of all draughts would have to have very large metacentric heights much above the Rule minimum. Fortunately as stated previously such low hatch coamings are not used in practice because of the other requirements. And that fact (as stated in []) seems to be the main reason for the absence of inland container ship accidents in the beam winds. Figure 5. Minimal metacentric height for typical European inland container vessel (calculated according to UNECE Rules) It is important to stress here the present practice in inland container transportation. The containers at least in European inland waterways are mainly carried as non-fixed. The hatch coamings on inland container vessels are (because of the structural requirements) in most cases over m high which is considerably higher than prescribed by the stability Rules. So special attentions should be focused on such custom vessels complying with those usual particularities. The probability curves for the Rhine and the Danube vessels for different hatch coaming heights correlated to the minimal metacentric heights prescribed by the Rules are presented in Figures 6 and 7. This comparison leads to several important conclusions. The Rhine vessels are indeed safer in beam wind than the corresponding Danube vessels. The custom Rhine vessels (carrying non-fixed containers having hatch coamings over m high) are safe enough if their metacentric height is at the minimum prescribed by the Rules. However if the hatch coaming height is at its very minimum (0.4 m) the metacentric height should be increased for more than 30 cm over the value prescribed by the Rules to get the acceptable probabilities of flooding. In the case of fixed containers the situation is even worse. The metacentric height of the Rhine vessels in this case should be increased for at least 30 cm above the value required by the Rules for any value of hatch coaming height. The custom Danube vessels (carrying non-fixed containers having the hatch coamings over m high) are not safe enough if their metacentric height is at the minimum prescribed by the Rules. Even more the Danube vessel cannot be made safe enough for any hatch coaming height if her metacentric height is at the minimum prescribed by the Rules. This implies for both cases: fixed and non-fixed containers although the situation in the case of non-fixed containers is considerably better. The custom Danube vessels could be made safe enough if their minimal metacentric height is increased for some 0 cm. Figure 8 presents the probability of flooding as a function of vessel draught for different metacentric height and for the very minimal hatch coaming height of 0.4 m. It shows clearly the unacceptability of such low Figure 6. The Rhine vessel: probability curves for different hatch coaming heights correlated to Rule minimal metacentric height Figure 7. The Danube vessel: probability curves for different hatch coaming heights correlated or Rule minimal metacentric height Figure 8. The probability of flooding in the beam wind for H c = 0.4 m and different metacentric heights Figure 9 presents the probability of flooding as a function of vessel draught for different hatch coaming heights and constant value of metacentric height. The metacentric height is fixed to m as the minimal value for common case of non-fixed containers. It proves that the vessels of minimal hatch coaming height of 0.4 m are extremly unsafe. The figure also shows that the FME Transactions VOL. 36 No

6 custom vessels having hatch coaming height over a meter are safe enough if their draught is over.5 m. The Danube vessels of small draught however could not reach the desired safety with any technically applicable hatch coaming height. Figure 9. The probability of flooding in beam wind for MG = m and different hatch coaming heights 5. CONCLUSIONS A series of inland container vessels of the same length and breadth loaded with the same (maximal) number of containers but varying in draught were exposed to the beam gusting wind of the mean speed prescribed by the stability rules. The nonlinear rolling of the vessel due to wind gusts was calculated and from these results the probability that the open container hold would be flooded was found. It was demonstrated that in such conditions the vessels of smaller draught would always have the higher risks of flooding. It was found in the previous investigation [-3] that the existing inland container vessel stability regulations are not strict enough so that the vessel complying with the minimal rule requirements have too high risks of flooding in the beam wind. In addition to that disturbing aspect of the rules the present investigation demonstrated that the rules do not account properly the changes in the vessel draught. The decrease of draught for the vessel complying with the minimal stability requirements always implies the increased risk of flooding and eventual capsizing. The earlier investigation indicated that the main reason for the lack of accidents connected to the insufficiency of regulations is the fact that the usual (custom) vessels because of the structural (and other) requirements do have hatch coamings considerably higher than prescribed by the rules. The present investigation pointed that such custom vessels (having hatch coaming heights of over a meter) are safe enough if their design draught is over 3 m as usual on the Rhine. However for draughts of. m (as restricted on the Lower Danube) the vessels of custom hatch coaming heights would have unacceptably high risks of flooding. It seems that the present inland container vessel stability regulations have been tailored for the Rhine vessels of higher draughts and therefore do not account properly the vessels of smaller draughts suitable for the Danube. The container transport on the Rhine has a long tradition and great importance for the Western Europe so it is natural that the conditions on the Rhine were taken as a starting point for the rule development. However the shortcomings of the rules concerning small-draughted vessels could provoke a tragedy especially as is expected that the container transport on the Danube (for the reasons not to be elaborated here) increases rapidly in the oncoming years. Therefore the authors appeal to the appropriate authorities to reconsider the rules and overcome the pointed shortcomings. The obvious way to overcome the deficiency of the rules and to make the risks of flooding and capsize of small-draughted vessels (at least) as low as of the Rhine vessels is to prescribe the minimal requirements of the rules (minimal metacentric height minimal safety distance) dependant on the vessel draught. The present investigation indicates that the minimal metacentric height of the Danube vessels should be increased for at least 0 cm. However to make vessels of all draughts (for the usual case of non-fixed containers) safe enough from the probabilistic point of view the requirement of minimal hatch coaming height should not be left to the good practice of vessel designers. It should be considerably increased over the present minimal value and fixed by the rules to at least m. The main task of the novel approach employed in the present investigation is the development of the new risk-based ship safety standards. However before this long-term goal is achieved the method could be used in numerous other topics of ship safety. The present investigation seems to be a good demonstration of the ability of the method when applied to improve the existing ship safety regulations. AKNOWLEDGMENT The paper is a part of research Development of Riskbased Ship Stability Regulations for which the authors got The 007 Royal Institution of Naval Architects and Lloyd s Register Educational Trust SHIP SAFETY AWARD. The paper is also a part of a long-term project Development of New Generation of Inland Cargo Vessels executed by Department of Naval Architecture Faculty of Mechanical Engineering University of Belgrade financed by Serbian Ministry of Science (Contract No. TR-637A). REFERENCES [] Hofman M. and Bačkalov I.: Weather Criterion for Seagoing and Inland Vessels Some New Proposals in: Proceedings of International Conference on Marine Research and Transportation ICMRT Ischia (Gulf of Naples) pp [] Hofman M. Maksić I. and Bačkalov I.: Some Disturbing Aspects of Inland Vessel Stability Rules Journal of Ship Technology Vol. No. pp [3] Bačkalov I. Kalajdžić M. and Hofman M.: Inland Vessel Rolling Due to Severe Beam Wind a Step Towards a Realistic Model Probabilistic Engineering Mechanics submitted for publication. 56 VOL. 36 No 008 FME Transactions

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