6 Methodology

  6.1.1 Independent analysis uses the "constant displacement"/"lost buoyancy" method.

  6.1.2 Within the scope of damage stability analysis with the deterministic approach, depending on the subdivision of the ship, the result of applying the standard of damage as specified in the applicable requirements is the creation of a number of damage cases, where one or more compartments are open to sea.

  6.1.3 The compartment(s), once damaged, are not considered as contributing to the buoyancy of the ship. Consequently, a new condition of equilibrium occurs. In order to define the new equilibrium condition and to assess the stability of the ship after damage the lost buoyancy/constant displacement method is used.

  6.1.4 The new floating position can be determined by assuming that the damaged displacement is equal to the intact displacement (constant displacement) minus the weight of liquids which were contained in the damaged compartments.

  6.1.5 Due to the lost buoyancy of the damaged compartment(s), the remaining intact ship has to compensate by sinkage, heel and trim until the damaged displacement is reached. Once the equilibrium has been reached and the final waterline is determined, the metacentric height (GM), the righting lever curves (GZ) and the centre of gravity positions (KG), can be calculated in order to verify the stability of the ship against the applicable requirements.

  6.1.6 For the intermediate stages of flooding and the equalization with compartments cross-connected by small ducts, i.e. not opened to the sea directly, the added weight method is used.

 The arguments used in the calculation for the verification of damage stability are the following:

• .1 trim: The calculation should be done for the ship freely trimming;

• .2 heel angle at equilibrium: The heel angle at equilibrium, due to unsymmetrical flooding, should not exceed the maximum values as indicated in the applicable requirements. Concerning the range of positive righting levers (GZ), this should be calculated beyond the position of equilibrium to the extent as so required by the applicable requirements;

• .3 free surface of liquid: For the calculation of the position of the centre of gravity (KG), the metacentric height (GM) and the righting lever curves (GZ), the effect of the free surfaces of liquids (see section 6.5) should be taken into account;

• .4 immersion of weathertight and unprotected openings (see sections 6.7 and 10.1)
  Unprotected openings:
  The positive range of righting levers is calculated from the angle of equilibrium until the angle of immersion of the unprotected openings leading to intact spaces;
  Weathertight points: see paragraph 10.1.2;

• .5 progressive flooding through internal pipes: in case of damage of an internal pipe which is connected to an undamaged compartment, the undamaged compartment should also be flooded, unless arrangements are fitted (e.g. check valves or valves with remote means of control), which can prevent further flooding of the undamaged compartments;

• .6 permeabilities: care should be taken to apply the permeabilities as specified in the applicable regulations. Special attention should be paid in case compartments which are separated by weathertight boundaries are modeled as one compartment. This simplified method of modeling the compartments should apply only to compartments belonging to the same category (same permeability); and

• .7 heel angles for the calculation of the GZ curve: evaluation of damage stability criteria should generally be determined from data calculated over a range of angles from 0 to 60 degrees. It is recommended to use an increment not exceeding 5 degrees.

  6.3.1 In cases where the damage involves the cargo hold, it is assumed that cargo is flowing out and that water ingress starts. During the intermediate stages of flooding it is considered that both cargo and seawater are existing in the damaged tank (see section 9.3).

  6.3.2 At the final stage it is assumed that the cargo is completely lost and that the tank is filled with seawater up to the level of the waterline.

  6.3.3 The impact on the stability of the ship, due to the inflow and outflow of liquid cargo is also dependent on the following parameters:

• .1 the density of the cargo: liquid cargo with density greater than 0.95 t/m³ should be considered as heavy liquid cargo. In case of lesser vertical extent of damage, i.e. damage above the tank top (see appendix 4), the release of heavy liquid cargo might lead to large angle of heel on the intact side of the ship. Depending on intact draught and cargo tank filling level, outflow of cargo of lesser density may also cause heel to the opposite side; and

• .2 the permeability of the cargo space, taking into account that permeabilities smaller than those specified in the applicable rules can be applied, if justified.

  6.4.1 Permeability of a space means the ratio of the volume within that space, which should be assumed to be occupied by water to the total volume of that space. The total volume should be calculated to moulded lines, and no reduction in total volume should be taken into account due to structural members (i.e. stiffeners, etc.). Account of structural members is taken in the applicable permeabilities (see also MSC/Circ.406/Rev.1, paragraph 3.11).

  6.4.2 Depending on the applicable requirements, the permeabilities assumed for spaces flooded as a result of damage should be as shown in table 2.

  6.4.3 Whenever damage penetrates a tank containing liquids, it should be assumed that the contents are completely lost from that compartment and replaced by seawater up to the level of the final plane of equilibrium.

  6.4.4 Other figures for permeability may be used for the damaged case both during cargo run-off and the final equilibrium condition under the following provisions:

• .1 the detailed calculations and the arguments used for determining the permeability of the compartment(s) in question, is to be included in the damage stability booklet;

• .2 the water tightness/resistance to water pressure and the means by which internal fittings/material are secured to the tank should substantiate the use of such fittings/material in reducing the permeability of a compartment. Where a ship is fitted with significant quantities of cargo insulation, the permeabilities of the relevant cargo spaces and/or the void spaces surrounding such cargo spaces may be calculated by excluding the volume of insulation material in those spaces from the flooded volume, provided that the insulating material is shown to comply with the following conditions:

  • .1 it is impermeable to water under hydrostatic pressure at least corresponding to the pressure caused by the assumed flooding;

  • .2 it will not crush or break up due to hydrostatic pressure at least corresponding to the pressure caused by the assumed flooding;

  • .3 it will not deteriorate or change its properties over the long term in the environment anticipated in the space it is installed;

  • .4 it is highly resistant to the action of hydrocarbons, where relevant; and

  • .5 it will be adequately secured so that it will remain in position if subjected to collision damage and consequent displacement, distortion of its supporting and retaining structure, repeated rapid ingress and outflow of seawater and the buoyant forces caused by immersion following flooding;

• .3 the applied permeability should reflect the general conditions of the ship throughout its service life, rather than specific loading conditions; and

• .4 permeabilities other than those indicated in table 2 should be considered only in cases, where it is evident that there is a significant discrepancy between the values shown in the regulations and the actual values (i.e. due to specific tank structure or insulating material).

 With respect to the approval of actual loading conditions the following should be applied:

  6.5.1 The free surfaces of liquids lead to the increase of the centre of gravity (KG) and the reduction of the metacentric height (GM) and the righting arm (GZ curve) of the ship. Therefore corrections should be made, taking into account the change of the centre of gravity of the ship due to the moving of the centre of gravity of the liquids. Depending on the filling level, free surfaces can exist in tanks with consumable liquids, seawater ballast and liquid cargo.

  6.5.1.1 For consumable liquids account on the free surfaces should be taken whenever the filling level is equal to or less than 98 per cent:

• .1 In calculating the free surface effects in tanks containing consumable liquids, it should be assumed that for each type of liquid at least one transverse pair or a single centreline tank has a free surface and the tank or combination of tanks taken into account should be those where the effect of free surfaces is the greatest.

• .2 Taking into account subparagraph .1, the free surfaces should correspond to the maximum value attainable between the filling levels envisaged.

  6.5.1.2 During ballasting between departure and arrival condition, the correction for the free surfaces should correspond to the maximum value attainable between the filling levels envisaged. This applies also for the situation where in the departure condition the filling level of a ballast tank is 0 per cent and in the arrival 100 per cent (or the opposite).

  6.5.1.3 For the category of liquids referred to under paragraphs 6.5.1.1 and 6.5.1.2, intermediate loading conditions may be considered as an alternative, as deemed necessary, covering the stage where the free surfaces are the greatest. It may be calculated with varying free surface moments (i.e. actual liquid transfer moments), taking into account actual heel and trim, depending on the interval angles of the GZ curve. This is a more accurate method.

  6.5.1.4 Except as indicated in regulation 27(11)(v) of the 1988 Load Lines Protocol, for liquid cargo the effect of free surface should be taken into account for the filling level equal to or smaller than 98 per cent. If the filling level is fixed actual free surfaces can be applied. The following two methods can be used for the calculation of the GZ curve, taking into account the effect of the free surface moments for the intact compartments:

• .1 Calculation with constant effect of free surfaces, without taking into account the change in heel and trim, for the interval angles of the GZ curve.

• .2 Calculation with varying free surface moments, actual liquid transfer moments, taking into account actual heel and trim, depending on the interval angles of the GZ curve (see appendix 2).

  6.5.2 For the damaged compartments, whenever the damage is involving cargo tanks, account should be taken of the following:

• .1 the impact on the stability of the ship due to the outflow of cargo and ingress of seawater can be verified with the calculation of the intermediate stages of flooding (see section 9); and

• .2 at the final equilibrium the free surface correction should exclude the free surface moment of the lost cargo.

  6.5.3 The free surface effect should be calculated at an angle of heel of 5° for each individual compartment or as per paragraph 6.5.1.3.

  6.6.1 For the assumed damage and the resultant damage cases, the damage stability should be assessed for all anticipated conditions of loading and variations in draught and trim.

  6.6.2 Significant trim values (greater than 1% L_pp) can appear in the aft/fore part of the ship in the departure and arrival condition. In that case, damage cases involving the aft/fore part of the ship might be critical for achieving compliance with the applicable criteria. In order to limit the trim, ballast water is used during the voyage, as deemed necessary. Under the provision of paragraphs 6.5.1.2 and 6.5.1.3, for taking account of the free surface effect during ballasting, if intermediate stages of the voyage are considered, then the loading conditions representing these stages should be also calculated for damage stability.

  6.7.1 Down-flooding point is the lower edge of any opening through which progressive flooding may take place. Such openings should include air pipes, ventilators and those which are closed by means of weathertight doors or hatch covers and may exclude those openings closed by means of watertight manhole covers and flush scuttles, small watertight cargo tank hatch covers which maintain the high integrity of the deck, remotely operated watertight sliding doors, and sidescuttles of non-opening type.

  6.7.2 All openings through which progressive flooding may take place should be defined: both weathertight and unprotected. As an alternative, it might be accepted to consider only the most critical openings, which are considered to be the openings with the lowest vertical position and close to the side shell. Concerning the longitudinal position it depends on the aft or fore trim of the initial condition and the trim after damage at equilibrium. Unprotected openings should not be immersed within the minimum range of righting-lever curve required for the ship. Within this range, the immersion of any of the openings capable of being closed weathertight may be permitted.

  6.8.1 Cross-flooding time should be calculated in accordance with the Recommendation on a standard method for evaluating cross-flooding arrangements (resolutions MSC.245(83) or MSC.362(92), as appropriate).

  6.8.2 If complete fluid equalization occurs in 60 s or less, the equalized tank should be assumed flooded with the tanks initially to be flooded and no further calculations need to be carried out. Otherwise, the flooding of tanks assumed to be initially damaged and equalized tank should be carried out in accordance with section 9.2. Only passive open cross-flooding arrangements without valves should be considered for instantaneous cases.

  6.8.3 Where cross-flooding devices are fitted, the safety of the ship should be demonstrated in all stages of flooding (see sections 9.2 and 10). Cross-flooding equipment, if installed, should have the capacity to ensure that the equalization takes place within 10 min.

  6.8.4 Tanks and compartments taking part in such equalization should be fitted with air pipes or equivalent means of sufficient cross-section to ensure that the flow of water into the equalization compartments is not delayed.

  6.8.5 Spaces which are linked by ducts of a large cross-sectional area may be considered to be common, i.e. the flooding of these spaces should be interpreted as instantaneous flooding with the equalization of duration of less than 60 s.

  6.9.1 Progressive flooding is the flooding of compartments situated outside of the assumed extent of damage. Progressive flooding may extend to compartments, other than those assumed flooded, through down-flooding points (i.e. unprotected and weathertight openings), pipes, ducts, tunnels, etc.

  6.9.2 The flooding of compartment(s) due to progressive flooding occurring in a predictable and sequential manner through a down-flooding point which is submerged below the damage waterline may be permitted provided all intermediate stages and the final stage of flooding meet the required stability criteria.

  6.9.3 Minor progressive flooding through the pipes situated within the assumed extent of damage may be permitted by the Administration, provided the pipes penetrating a watertight subdivision have a total cross-sectional area of not more than 710 mm² between any two watertight compartments.

  6.9.4 If the opening (unprotected or fitted with a weathertight means of closure) connects two spaces, this opening should not be taken into account if the two connected spaces are flooded or none of these spaces are flooded. If the opening is connected to the outside, it should not be taken into account only if the connected compartment is flooded.