Dynamic Intact Stability Criteria Scope. General The aim of this report is to introduce dynamic criteria for the intact stability of ships which cover the phenomena of parametric roll and pure loss of stability on the wave crest. These phenomena can be related to alterations of the righting levers in wave crest and wave trough condition. The dynamic criteria proposed in this report shall be seen as additional criteria to the existing intact stability criteria and they should be applied for all types of ships covered by IMO- instruments. The dynamic criteria proposed in this report reflect the necessity of explicitly dealing with pure loss and parameric rolling which has become a problem for some types of ships. It is the clear intention of the dynamic criteria that all ships which are not affected by the latter phenonema can still be operated at the same stability standards as today..2 Principle of the Criteria Waves: H= 5.8m, L=98.6m.5 Waves: H= 5.8m, L=98.6m.8.6.4.2 -.2 -.4.5 -.5 -.6 -.8 - - -6-4 -2 2 4 6 -.5-6 -4-2 2 4 6 Still:GM=.75,A5=.239,hmax=.525 Crest:GM= -.69,A5= -.4,hmax=.72 Throu:GM= 2.723,A5=.54,hmax=.943 GM-Diff. Tr.-Cr.: 3.332 m Still:GM=.,A5=.534,hmax=.55 Crest:GM=.27,A5=.29,hmax=.67 Throu:GM= 3.548,A5=.836,hmax=.355 GM-Diff. Tr.-Cr.: 3.33 m Figure : Righting levers of a (RoRo) ship in still water, crest and trough conditions at the actual limiting GM according to the Intact Code (left) and for the same ship according to the Damage Stability Limit (right). The dynamic criteria reflect on the following two phenomena which may occur in rough weather: Pure loss of stability on the wave crest Excessive roll angles due to parametric excitation Recent research investigations have clearly shown that these phenomena can be related to alterations of the righting levers in wave crest and trough condition. These alterations, which can be expressed by the differences of the righting levers at trough and crest condition, are always related to a specific hull form. The energy introduced into that specific hull form in a seastate may be expressed by the alterations of the areas below the righting levers at trough and crest condition. This is illustrated in Fig., where the righting levers are presented for a typical modern hull form at stillwater, crest and trough condition. /7
The left picture shows the three righting lever curves at an initial stillwater GM according to the Intact Stability limit (GM is abt..75m), and the right picture shows the same righting lever curves for the damage stability limit (GM is abt.. m). At the Intact Limit, the ship has practically no stability on the crest at all and the vessel is exposed to large rolling amplitudes which might lead to a capsize, but at the actual damage stability limit, the situation on the crest is drastically improved and the occurence of large rolling amplitudes is reduced. Recent investigations have shown that the avoidance of large rolling amplitudes for a specific hull form requires still water stability limits that need to be expressed by the trough/crest alterations..5 Waves: H= 5.8m, L=98.6m.5 Waves: H= 5.8m, L=98.6m a4 diff.5 -.5 a 4.5 -.5 - - -.5-6 -4-2 2 4 6 Still:GM=.,A5=.534,hmax=.55 Crest:GM=.27,A5=.29,hmax=.67 Throu:GM= 3.548,A5=.836,hmax=.355 GM-Diff. Tr.-Cr.: 3.33 m -.5-6 -4-2 2 4 6 Still:GM=.,A5=.534,hmax=.55 Crest:GM=.27,A5=.29,hmax=.67 Throu:GM= 3.548,A5=.836,hmax=.355 GM-Diff. Tr.-Cr.: 3.33 m Figure 2: Areas below still water righting levers (left) and the area difference trough- crest (right) for the same ship as above. This is expressed by Fig. 2 where for the same ship as in Fig. the righting levers are plotted (Damage Stabiliy Limit). The left picture shows the area under the still water righting lever curve a 4, and the left picture shows the area difference between the righting levers in trough and crest condition. It can be shown that this area difference is a function of the hull form only and does practically not depend on the initial GM (or ZCG, respectively). The stillwater area does in fact depend on the initial GM. Therefore, the aim of the dynamic criteria proposed here is to ensure that the initial minimum stillwater GM to be attained for a specific hull form is sufficient to compensate the crest trough alteration in a given reference wave. This means that the stillwater area should be proportional to the crest/trough alteration which is practically a constant value for a specific hull form. If a hull form has small or even no alterations (e.g. a full block coefficient bulker or a pontoon), then the stillwater area requirement from the dynamic criteria would amount practically to zero and the ship can be operated at the actual Intact Code limiting values. If a hull form has extremely large area alterations, this can result in higher initial stillwater GM- requirements from the dynamic criteria than from the existing Intact Stability Code. It may be possible that the actual damage stability limits lead to still water areas that are already sufficient, but it may also be possible that a specific hull form requires initial stillwater GM values that are slightly above the damage stability limit. In this case, the designer has three options to fulfill the dynamic criteria: This holds if secondary effects which cover the equilibrium trim influence by the term BG tan ϑ can be disregarded, which is practically the case. However, even if this influence can be noted it is small and it does not affect the results in principle. 2/7
Accept larger initial GM Reduce crest- trough alterations by alterations of the hull form with respect to increased stability on the crest reduced stability on the trough Recent investigations have shown that the competitiveness of the ships is not affected if the proper design measures are taken..3 Internal liquids and openings It should further be noted that the dynamic background of the criteria requires a different treatment of internal liquids than the actual static criteria of the Intact Code. Dynamically, internal liquids do in most cases reduce a rolling motion, whereas in a statical condition, internal liquids do increase a heeling angle due to fluid shifting moments. Therefore, to be on the safe side, the dynamic criteria reflect only to a solid ZCG (or GM, respectively) and applying the criteria will result in a minimum GM- Curve (or maximum ZCG) for the Solids only. When a specific load case will be checked against the dynamic criteria, no free surface corrections need to be made. For compliance with the existing stability limits of the intact code, free surfaces have to be accounted for anyway. As it is the aim of the dynamic criteria to judge upon the hull form only, openings shall not be considered. Otherwise it would be possible to reduce the trough area by simply introducing an opening which becomes submerged. This is clearly not intended by the dynamic criteria. Openings are sufficiently treated by the existing static intact criteria of the Code. When the righting levers for the dynamic criteria are determined, all weathertight contributions to buoyancy of the hull as defined by relevant codes have to be taken into account..4 Background of the Criteria Reference is made to several papers presented in the bibliography which give a detailed overview about the related research projects and results. The criteria have been developed on the basis of direct calculation of capsizing frequencies in rough weather. About 2 different recently built ships have been analyzed by the numerical code ROLLS in a German BMBF- funded research project. The code was validated by several model tests and found to be able to determine capsizing events related to parametric rolling or pure loss of stability with sufficient accuracy. The dynamic criteria suggested in this report are based on the evaluation of these direct computations and are kept simple enough to be applied practically in the design process as well as for the evaluation. 2 Structure of the new Criteria 2. General The dynamic criteria are based on the determination of three righting lever curves (ref. Fig. ) which have to be determined for still water, crest and trough condition. All righting levers have to be determined on a free trimming basis. 3/7
2.2 Dynamic Criteria for Pure Loss and Parametric Rolling The areas under the stillwater righting lever from Degree to 5 Degree (A5 Still ) and from Degree to 4 Degree (A4 Still ) shall take at least the following value: A5 Still = [.5](A5 T rough A5 Crest ) () where: A4 Still = [.75](A4 T rough A4 Crest ) (2) A5 Still means the area under the still water righting lever up to an angle of 5 Degree A5 T rough means the area under the wave trough righting lever up to an angle of 5 Degree 4 Still means the area under the still water righting lever up to an angle of 4 Degree 4 T rough means the area under the wave trough righting lever up to an angle of 4 Degree 4 Crest means the area under the wave crest righting lever up to an angle of 4 Degree The areas shall be calculated including all negative contributions if the righting lever is below zero. The area shall always be calculated to the specified angle, regardless if an opening might be submerged or not. When the righting levers are determined, the free surface effect of partly filled tanks or anti- heeling devices must not be taken into account, ZCG is to be taken from the solids only. The proportional factors [.5] and [.75], respectively, were determined from systematic simulations of ships in heavy weather. For about 2 different ships, the theoretical capsizing frequency was determined, and a statistical analysis of all the data has shown that if the proportional factors of [.5] and [.75] are used, a uniform safety level is achieved by the a.m. formula which reprents the safety level of the current fleet in operating condition. Because it should be kept in mind that most of the ships are not operated at the intact limit, but acoording to the damage stability limit or at other conditions resulting from operational requirements. So the a.m. formulae should be seen as an attempt to give all vessels minimum intact stability requirements that represent a uniform safety level on one hand and to adjust this safety level to the existing fleet. It is further important to note that sufficient safety against parametric rolling or pure loss can only be achieved by the combination of these criteria. The a 5 - criterion ensures sufficient initial stability to avoid the start of a parametric roll sequence. The a 4 - criterion ensures sufficient righting moment if a larger rolling angle has actually occured. In combination, both criteria represent a uniform and sufficient safety level. 4/7
3 Determination of the righting levers λ L/2 f. A.P. + λ/2 Trough Crest H L/2 f. A.P. A.P. L F.P. Figure 3: Determination of the critical wave for crest and trough condition. Note that the critical wave has to be determined for the ship in full equilibrium with respect to draft, trim and heel which has been omitted in this figure for simplification reasons. The crest condition shall be determined as follows, ref. Fig. 3: The wavy surface shall be represented by a sinusoidal wave which is defined by wave length λ, a wave height H and a crest position x Crest. The wave crest shall be always be positioned at L/2 f. A.P. The critical wave length λ and wave height H have to be selected for this fixed crest position as that critical combination of λ and H which lead to the largest alteration of initial metacentric height GM at full equilibrium with respect to draft, trim and heel between crest and trough condition, where the trough condition is defined by the same values for λ and H, but the position of the wave crest amounts to x T rough = x Crest + λ/2. The wave height H shall be selected for a given wave length λ according to the following formula: H(λ) =.35λ.756 (3) The formula was derived by regression from the North Atlantic Wave Spectrum as a 9% quantil: 9% of all waves in that area are below the limiting height as given by the a.m. formula. The righting levers in the trough condition shall be determined for the same critical values of λ and H found for the crest condition, but the crest is always to be positioned at λ/2 before L/2: x T rough = x Crest + λ/2 (4) It was found by model experiments as well as by numerical simulations, that this simplified procedure, which is still based on the determination of static righting levers, reflects the most important dynamic effects with a sufficient accuracy without making the calculation procedure too complicated. An alternative to the a.m. procedure would be not to select the trim from the equilibrium condition, but from the actual pitching phase and amplitude which could be determined from direct seakeeping calculations. However, this alternative procedure is more complex and does not lead to significant differences in the results, which makes the simplified approach more appropriate. However, the simplified approach is only valid for the given position of the wave crest, if this position is varied, then the correct pitching amplitude and phase must be used for the calculations to obtain the correct results. 4 Calculation procedure, summarized The following procedure should be applied for each draft which is relevant for the limiting GM- required or KGMAX- Curve: 5/7
Determine the critical wave parameters λ and H which lead to the largest alterations of GM between the crest condition and the corresponding trough For this critical wave, determine the area up to 5 Deg (or 4, respectively) taking into account all negative area contributions. Any downflooding angle must not be taken into account. Calculate the area difference trough-crest. Check if stillwater righting lever area is larger or equal to the limiting values as stated above. The picture below shows a calculation example for the A4 Crest (left) and the final righting levers of the same ship as in the figures above which fulfill the dynamic criteria suggested (right). Waves: H= 5.8m, L=98.6m 2 Waves: H= 5.8m, L=98.6m, GM=.345.8.5.6.4.2 -.2 -.4 -.6 -.8 a a2 Downflooding Angle.5 -.5 - -.5 - -6-4 -2 2 4 5 6 Still:GM=.75,A5=.239,hmax=.525 Crest:GM= -.69,A5= -.4,hmax=.72 Throu:GM= 2.723,A5=.54,hmax=.943 GM-Diff. Tr.-Cr.: 3.332 m -2-6 -4-2 2 4 6 Still:A5.53,A4=.445 Crest:A5.22,A4=.272 Throu:A5.29,A4=.733 A5-Diff *.5 :.53 m A4-Diff. *.75 :.346 m Passed Figure 4: Calculation example for the determination of A4 Crest (left). The resulting area is a+a2= -.4 mrad. The area must be calculated to 4 Degree and not be limited by the angle of downflooding. The right picture shows the righting lever curves which fulfill the dymamic stability limits. 5 References BLUME, P. (987) Development of New Stability Criteria for Modern Dry Cargo Vessels Proceedings PRADS Conference 987 CRAMER, H., KRUEGER, S. (2) Numerical capsizing simulations and consequences for ship design JSTG 2, Springer CRAMER, H., HINRICHS, R., KRUEGER, S.: (24) Performance Based Approaches for the Evaluation of Intact Stability Problems Proceedings PRADS Conference 24, Travemuende HASS, C. (2) Darstellung des Stabilitaetsverhaltens von Schiffen verschiedener Typen und Groesse mittels statischer Berechnung und Simulation Diploma Thesis, TU Hamburg- Harburg, in preparation KROEGER, P. (987) Simulation der Rollbewegung von Schiffen im Seegang Bericht Nr. 473, Institut fuer Schiffbau der Universitaet Hamburg KRUEGER, S.: (998) Performance Based Stability DCAMM 22, Lyngby SOEDING, H. (987) Ermittlung der Kentergefahr aus Bewegungssimulationen Schiffstechnik Band 34 SOEDING, H. (988) Berechnung der Bewegungen und Belastungen von SWATH-Schiffen und Katamaranen im Seegang Bericht Nr. 483, Institut fuer Schiffbau der Universitaet Hamburg 6/7
SOEDING, H. (2) Global Seaway Statistics Report Nr. 6, TU Hamburg- Harburg, Schriftenreihe Schiffbau 7/7