Part II - Stability

4.3 Intact Stability and Information^footnote

(1) Every ship to which this Code applies shall be inclined upon its completion and the elements of its stability determined.

(2) Where any alterations are made to a ship so as to materially affect the stability information supplied to the master-

• (a) amended stability information shall be provided;

• (b) if necessary the ship shall be re-inclined; and

• (c) the ship shall be re-inclined if anticipated deviations exceed one of the values specified in Section (3)(b).

(3) At periodical intervals not exceeding five years-

• (a) a lightweight survey shall be carried out on all passenger ships to verify any changes in lightship displacement and longitudinal centre of gravity; and

• (b) the ship shall be re-inclined whenever, in comparison with the approved stability information, a deviation from the lightship displacement exceeding 2% or a deviation of the longitudinal centre of gravity exceeding 1% of L_sis found or anticipated^footnote.

(4) In applying this section due regard shall be given to the Intact Stability Code 2008 as defined in Chapter 2 of this Code.

4.4 Stability Information to be supplied to the Master^footnote

(1) The master shall be supplied with such stability information satisfactory to the Administration as is necessary to enable him by rapid and simple processes to obtain accurate guidance as to the stability of the ship under varying conditions of service and a copy of the stability information shall be furnished to the Administration.

(2) Information shall be provided to the master-

• (a) in a form that is approved by the Administration or a Recognised Organisation; and

• (b) such information, and loading information also related to ship strength when required under Section (1), shall be carried onboard at all times together with evidence that the information has been approved by the Administration.

(3) The information shall include-

• (a) curves or tables of minimum operational metacentric height (GM) versus draught which assures compliance with the relevant intact and damage stability requirements, alternatively corresponding curves or tables of the maximum allowable vertical centre of gravity (KG) versus draught, or with the equivalents of either of these curves;

• (b) instructions concerning the operation of cross-flooding arrangements; and

• (c) all other data and aids which might be necessary to maintain the required intact stability and stability after damage.

(4) The stability information shall show the influence of various trims in cases where the operational trim range exceeds +/- 0.5% of L_s.

(5) For ships which have to fulfil the stability requirements of Part II of this Chapter, information referred to in Section (2) is determined from considerations related to the subdivision index, in the following manner-

• (a) minimum required GM (or maximum permissible vertical position of centre of gravity KG) for the three draughts d_s, d_p and d₁ are equal to the GM (or KG values) of corresponding loading cases used for the calculation of survival factor s_i;

• (b) for intermediate draughts, values to be used shall be obtained by linear interpolation applied to the GM value only between the deepest subdivision draught and the partial subdivision draught and between the partial load line and the light service draught respectively. Intact stability criteria shall also be taken into account by retaining for each draft the maximum among minimum required GM values or the minimum of maximum permissible KG values for both criteria; and

• (c) if the subdivision index is calculated for different trims, several required GM curves shall be established in the same way.

(6) When curves or tables of minimum operational metacentric height (GM) versus draught are not appropriate, the master shall ensure that the operating condition does not deviate from a studied loading condition, or verify by calculation that the stability criteria are satisfied for this loading condition.

(7) In applying this section due regard shall be had to the Intact Stability Code as defined in Chapter 2 of this Code.

4.5 Required Subdivision Index R^footnote

(1) The subdivision of a ship is considered sufficient if the attained subdivision index A, determined in accordance with section 4.6, is not less than the required subdivision index R calculated in accordance with this regulation and if, in addition, the partial indices A_s, A_p and A_l are not less than 0.9R for passenger ships.

(2) For all passenger ships to which the damage stability requirements of this Chapter apply, the degree of subdivision to be provided shall be determined by the required subdivision index R, as follows-

• 

• where:

• N = N₁ + 2N₂;

• N₁ = number of persons for whom lifeboats are provided^footnote; and

• N₂ = number of persons (including officers and crew) the ship is permitted to carry in excess of N₁.

(3) Where the conditions of service are such that compliance with Section (2) on the basis of N = N₁ + 2N₂ is impracticable and where the Administration considers that a suitably reduced degree of hazard exists^footnote, a lesser value of N may be taken but in no case shall the value be less than N = N₁ + N₂.

4.6 Attained Subdivision Index A

(1) The attained subdivision index A is obtained by the summation of the partial indices A_s, A_p and A_l, (weighted as shown) calculated for the draughts d_s, d_p and d_l defined in Chapter 2 in accordance with the following formula-

A = 0.4A_s + 0.4A_p + 0.2A_i

(2) Each partial index is a summation of contributions from all damage cases taken in consideration, using the following formula-

A = Σp_is_i

• where-

  • i represents each compartment or group of compartments under consideration;

  • p_i accounts for the probability that only the compartment or group of compartments under consideration may be flooded, disregarding any horizontal subdivision, as defined in section 4.7; and

• s_i accounts for the probability of survival after flooding the compartment or group of compartments under consideration, and includes the effect of any horizontal subdivision, as defined in section 4.8.

(3) In the calculation of A-

• (a) the level trim shall be used for the deepest subdivision draught and the partial subdivision draught;

• (b) the actual service trim shall be used for the light service draught; and

• (c) if in any service condition, the trim variation in comparison with the calculated trim is greater than 0.5% of L_s, one or more additional calculations of A shall be submitted for the same draughts but different trims so that, for all service conditions, the difference in trim in comparison with the reference trim used for one calculation shall be less than 0.5% of L_s.

(4) When determining the positive righting lever (GZ) of the residual stability curve, the displacement used shall be that of the intact condition; that is, the constant displacement method of calculation shall be used.

(5) The summation indicated by the above formula shall be taken over the ship’s subdivision length (L_s) for all cases of flooding in which a single compartment or two or more adjacent compartments are involved. In the case of unsymmetrical arrangements, the calculated A value shall be the mean value obtained from calculations involving both sides; alternatively, it shall be taken as that corresponding to the side which evidently gives the least favourable result.

(6) Wherever wing compartments are fitted-

• (a) contribution to the summation indicated by the formula shall be taken for all cases of flooding in which wing compartments are involved;

• (b) additionally, cases of simultaneous flooding of a wing compartment or group of compartments and the adjacent inboard compartment or group of compartments, but excluding damage of transverse extent greater than one half of the ship breadth B, may be added; and

• (c) for the purpose of this regulation, transverse extent is measured inboard from ship’s side, at right angle to the centreline at the level of the deepest subdivision draught.

(7) In the flooding calculations carried out according to the regulations-

• (a) only one breach of the hull and only one free surface need to be assumed; and

• (b) the assumed vertical extent of damage is to extend from the baseline upwards to any watertight horizontal subdivision above the waterline or higher.

• provided however, if a lesser extent of damage shall give a more severe result, such extent shall be assumed.

(8) If pipes, ducts or tunnels are situated within the assumed extent of damage, arrangements shall be made to ensure that progressive flooding cannot thereby extend to compartments other than those assumed flooded. However, the Administration may permit minor progressive flooding if it is demonstrated that its effects can be easily controlled and the safety of the ship is not impaired.

4.7 Calculation of the Factor p_i

(1) The factor p_i for a compartment or group of compartments shall be calculated in accordance with this section using the following notations-

• j = the aftmost damage zone number involved in the damage starting with No.1 at the stern;

• n = the number of adjacent damage zones involved in the damage;

• k = is the number of a particular longitudinal bulkhead as barrier for transverse penetration in a damage zone counted from shell towards the centre line; the shell has k = 0;

• x1 = the distance from the aft terminal of L_s to the aft end of the zone in question;

• x2 = the distance from the aft terminal of L_s to the forward end of the zone in question;

• b = the mean transverse distance in metres measured at right angles to the centreline at the deepest subdivision load line between the shell and an assumed vertical plane extended between the longitudinal limits used in calculating the factor p_i and which is a tangent to, or common with, all or part of the outermost portion of the longitudinal bulkhead under consideration; this vertical plane shall be so orientated that the mean transverse distance to the shell is a maximum, but not more than twice the least distance between the plane and the shell; if the upper part of a longitudinal bulkhead is below the deepest subdivision load line the vertical plane used for determination of b is assumed to extend upwards to the deepest subdivision waterline; in any case, b is not to be taken greater than B/2.

  • If the damage involves a single zone only:

  • p_i = p(x1_j , x2_j)·[r(x1_j , x2_j, b_k) – r(x1_j , x2_j, b_k-1)]

• If the damage involves two adjacent zones:

• p_i = p(x1_j , x2_j+1)·[r(x1_j , x2_j+1, b_k) – r(x1_j , x2_j+1, b_k-1)]
  • - p(x1_j , x2_j)·[r(x1_j , x2_j, b_k) – r(x1_j , x2_j, b_k-1)]
  • - p(x1_j+1 , x2_j+1)·[r(x1_j+1 , x2_j+1, b_k) – r(x1_j+1 , x2_j+1, b_k-1)]

• If the damage involves three or more adjacent zones:

• p_i = p(x1_j , x2_j+n-1)·[r(x1_j , x2_j+n-1, b_k) – r(x1_j , x2_j+n-1, b_k-1)]
  • - p(x1_j , x2_j+n-2)·[r(x1_j , x2_j+n-2, b_k) – r(x1_j , x2_j+n-2, b_k-1)]
  • - p(x1_j+1 , x2_j+n-1)·[r(x1_j+1 , x2_j+n-1, b_k) – r(x1_j+1 , x2_j+n-1, b_k-1)]

  • + p(x1_j+1 , x2_j+n-2)·[r(x1_j+1 , x2_j+n-2, b_k) – r(x1_j+1 , x2_j+n-2, b_k-1)]

• and where r(x1, x2, b₀) = 0

When L_s≤ L*:

• 

• 

• b₁₂ = b₀

When L_s>L^*:

• 

• 

• 

• 

• 

• 

• 

• 

• The non-dimensional damage length:

• 

• The normalised length of a compartment or group of compartments J_nshall be taken as the lesser of J and J_m

(3) Where neither limit of the compartment or group of compartments under consideration coincides with the aft or forward terminals-

• J≤J_k:

• p(x1,x2) = p₁ = J²(b₁₁J + 3b₁₂)

• J>J_k

• p(x1,x2) = p₂ = b₁₁J_k³ + (b₁₁J - b₁₂)J_k² + b₁₂JJ_k b₂₁(J_n³ - J_k³) + (b₂₁J- b₂₂)(J_n² - J_k²) + b₂₂J(J_n - J_k)

(4) Where the aft limit of the compartment or group of compartments under consideration coincides with the aft terminal or the forward limit of the compartment or group of compartments under consideration coincides with the forward terminal-

• J≤J_k:

  • p(x1, x2) = (p₁ + J)

• J>J_k:

  • p(x1, x2) = (p₂ + J)

(5) Where the compartment or groups of compartments considered extends over the entire subdivision length (L_s)-

• p(x1, x2) = 1

(6) The factor r(x1, x2, b) shall be determined by the following formulae-

• r(x1, x2, b) = 1 - (1 - C) ·

where-

• C = 12 · J_b · (-45 · J_b + 4); and

• 

(7) Where the compartment or groups of compartments considered extends over the entire subdivision length (L_s)-

• G = G₁ = b₁₁J_b² + b₁₂J_b

(8) Where neither limits of the compartment or group of compartments under consideration coincides with the aft or forward terminals-

• G = G₂ = b₁₁J₀³ + (b₁₁J - b₁₂)J₀² + b₁₂JJ₀

where-

• J₀ = min(J,J_b)

(9) Where the aft limit of the compartment or group of compartments under consideration coincides with the aft terminal or the forward limit of the compartment or group of compartments under consideration coincides with the forward terminal-

• G = (G₂ + G₁ · J)

4.8 Calculation of the Factor s_i

(1) The factor s_i shall be determined for each case of assumed flooding, involving a compartment or group of compartments, in accordance with the following notations and the provisions in this section, where-

• θ_e is the equilibrium heel angle in any stage of flooding, in degrees;

• θ_v is the angle, in any stage of flooding, where the righting lever becomes negative, or the angle at which an opening incapable of being closed weathertight becomes submerged;

• GZ_max is the maximum positive righting lever, in metres, up to the angle θ_v;

• Range is the range of positive righting levers, in degrees, measured from the angle θ_e.; the positive range shall be taken up to the angle θ_v;

• Flooding stage is any discrete step during the flooding process, including the stage before equalisation (if any) until final equilibrium has been reached.

(2) The factor s_i for any damage case at any initial loading condition, d_i, shall be obtained from the formula-

• s_i = minimum { s_{intermediate,i} or s_final,i · s_mom,i }

where-

(3) The factor s_{intermediate, i} shall be taken as the least of the s-factors obtained from all flooding stages including the stage before equalisation, if any, and shall be calculated as follows-

• 

where-

• GZ_max is not to be taken as more than 0.05 metres and Range as not more than 7°;
• s_intermediate = 0, if the intermediate heel angle exceeds 15º; and
• the time for equalisation shall not exceed 10 minutes where cross-flooding fittings are required.

(4) The factor s_final,i shall be obtained from the formula-

• 

where:

• GZ_max is not to be taken as more than 0.12 metres;
• Range is not to be taken as more than 16°;
• K = 1 if θ_e ≤ θ_min
• K = 0 if θ_e ≥ θ_max
• otherwise,
  • and where:
    • θ_min is 7° for passenger ships; and
    • θ_max is 15° for passenger ships.

(5) The factor s_mom,i shall be calculated at the final equilibrium from the formula-

• 

where:

• Displacement is the intact displacement at the subdivision draught;
• M_heel is the maximum assumed heeling moment as calculated in accordance with Section 4.1; and
• S_mom,i ≤ 1.

(6) The heeling moment M_heel shall be calculated as follows-

M_heel = maximum{M_passenger or M_wind or M_{survival craft}}

(7) M_passenger is the maximum assumed heeling moment resulting from movement of passengers, and shall be obtained as follows-

• (a) by the formula

  • M_passenger = (0.075 · N_p) · (0.45 · B) (tm)

• where-

  • N_p is the maximum number of passengers permitted to be onboard in the service condition corresponding to the deepest subdivision draught under consideration; and

  • B is the beam of the ship.

• (b) alternatively, the heeling moment may be calculated assuming the passengers are distributed with 4 persons per square metre on available deck areas towards one side of the ship on the decks where muster stations are located and in such a way that they produce the most adverse heeling moment and in doing so, a weight of 75 kg per passenger shall be assumed.

(8) M_wind is the maximum assumed wind force acting in a damage situation calculated in accordance with the following formula-

• M_wind = (P · A · Z) / 9,806 (tm)

where:

• P = 120 N/m²;
• A = projected lateral area above waterline;
• Z = distance from centre of lateral projected area above waterline to T/2; and
• T = ship’s draught, d_i.

(9) M_{Survivalcraft} is the maximum assumed heeling moment due to the launching of all fully loaded davit-launched survival craft on one side of the ship and it shall be calculated using the following assumptions-

• (a) all lifeboats and rescue boats fitted on the side to which the ship has heeled after having sustained damage shall be assumed to be swung out fully loaded and ready for lowering;

• (b) for lifeboats which are arranged to be launched fully loaded from the stowed position, the maximum heeling moment during launching shall be taken;

• (c) a fully loaded davit-launched liferaft attached to each davit on the side to which the ship has heeled after having sustained damage shall be assumed to be swung out ready for lowering;

• (d) persons not in the life-saving appliances which are swung out shall not provide either additional heeling or righting moment; and

• (e) life-saving appliances on the side of the ship opposite to the side to which the ship has heeled shall be assumed to be in a stowed position.

(10) Unsymmetrical flooding shall be kept to a minimum consistent with the efficient arrangements in accordance with the following provisions-

• (a) where it is necessary to correct large angles of heel, the means adopted shall, where practicable, be self-acting, but in any case where controls to equalisation devices are provided they shall be operable from above the bulkhead deck;

• (b) these fittings together with their controls shall be acceptable to the Administration^footnote and suitable information concerning the use of equalisation devices shall be supplied to the master of the ship;

• (c) tanks and compartments taking part in such equalisation shall be fitted with air pipes or equivalent means of sufficient cross-section to ensure that the flow of water into the equalisation compartments is not delayed.

(11) In all cases, s_i shall be taken as zero in those cases where the final waterline, taking into account sinkage, heel and trim, immerses-

• (a) the lower edge of openings through which progressive flooding may take place and such flooding is not accounted for in the calculation of factor s_i; such openings shall include air-pipes, ventilators and openings which are closed by means of weathertight doors or hatch covers; and

• (b) any part of the bulkhead deck in passenger ships considered a horizontal evacuation route for compliance with Chapter II-2 of SOLAS.

(12) The factor s_i shall be taken as zero if, taking into account sinkage, heel and trim, any of the following occur in any intermediate stage or in the final stage of flooding-

• (a) immersion of any vertical escape hatch in the bulkhead deck intended for compliance with Chapter II-2 of SOLAS;

• (b) any controls intended for the operation of watertight doors, equalisation devices, valves on piping or on ventilation ducts intended to maintain the integrity of watertight bulkheads from above the bulkhead deck become inaccessible or inoperable; and

• (c) immersion of any part of piping or ventilation ducts carried through a watertight boundary that is located within any compartment included in damage cases contributing to the attained index A, if not fitted with watertight means of closure at each boundary,

• provided however that where compartments assumed flooded due to progressive flooding are taken into account in the damage stability calculations multiple values of s_{intermediate,i} may be calculated assuming equalisation in additional flooding phases.

(13) Except as provided in section 4.8(12)(a), openings closed by means of watertight manhole covers and flush scuttles, small watertight hatch covers, remotely operated sliding watertight doors, side scuttles of the non-opening type as well as watertight access doors and hatch covers required to be kept closed at sea need not be considered.

(14) Where horizontal watertight boundaries are fitted above the waterline under consideration the s-value calculated for the lower compartment or group of compartments shall be obtained by multiplying the value as determined in section 4.8(2) by the reduction factor v_m according to section 4.8(15), which represents the probability that the spaces above the horizontal subdivision shall not be flooded.

(15) The factor v_m shall be obtained from the formula-

• v_m = v(H_{j, n, m,} d) - v(H_{j, n, m-1,}d)

where-

(16) The factors v(H_{j, n, m,} d) and v(H_{j, n, m-1}, d) shall be obtained from the formulae-

• v(H, d) = , if (H_m - d) is less than, or equal to 7.8 metres;

• v(H, d) = in all other cases,

where-

(17) In general, each contribution dA to the index A in the case of horizontal subdivisions is obtained from the formula-

• dA = p_i · [ν₁ · s_min1 + (ν₂ — ν₁) · s_min2 + ....+(1 — ν_m-1) · s_{min m}]

where

4.9 Permeability

(1) For the purpose of the subdivision and damage stability calculations of the regulations, the permeability of each compartment or part of a compartment shall be as follows-

(2) Other figures for permeability may be used if substantiated by calculations.

4.10 Requirements Concerning Passenger Ship Stability

(1) A passenger ship intended to carry 36 or more persons shall be capable of withstanding damage along the side shell to an extent specified in Section (2) and compliance with this section shall be achieved by demonstrating that s_i, as defined in section 4.8(2), is not less than 0.9 for the three loading conditions on which is based the calculation of the subdivision index.

(2) The damage extent to be assumed when demonstrating compliance with section 4.10(1), shall be dependent on both N and L_s, as defined in Chapter 2 and Section 4.5(2) respectively, such that-

• (a) the vertical extent of damage is to extend from the ship’s moulded baseline to a position up to 12.5 metres above the position of the deepest subdivision draft as defined in Chapter 2 unless a lesser vertical extent of damage were to give a lower value of si, in which case this reduced extent shall be used;

• (b) where 400 or more persons shall be carried, a damage length of 0.03L_s but not less than 3 metres shall be assumed at any position along the side shell, in conjunction with a penetration inboard of 0.1B but not less than 0.75 m measured inboard from the ship side, at right angles to the centreline at the level of the deepest subdivision draught;

• (c) where less than 400 persons are carried, damage length shall be assumed at any position along the shell side between transverse watertight bulkheads provided that the distance between two adjacent transverse watertight bulkheads is not less than the assumed damage length; if the distance between adjacent transverse watertight bulkheads is less than the assumed damage length, only one of these bulkheads shall be considered effective for the purpose of demonstrating compliance with section 4.10(1);

• (d) where 36 persons are carried, a damage length of 0.015L_s but not less than 3 metres shall be assumed, in conjunction with a penetration inboard of 0.05B but not less than 0.75 metres; and

• (e) where more than 36, but fewer than 400 persons are carried the values of damage length and penetration inboard, used in the determination of the assumed extent of damage, shall be obtained by linear interpolation between the values of damage length and penetration which apply for ships carrying 36 persons and 400 persons as specified in sections 4.10(2)(d) and 4.10(2)(b).