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 is to 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-

• sintermediate,i	is the probability to survive all intermediate flooding stages until the final equilibrium stage, and is calculated in accordance with subsection 3;
  sfinal,i	is the probability to survive in the final equilibrium stage of flooding, calculated in accordance with subsection 4; and
  smom,i	is the probability to survive heeling moments, and is calculated in accordance with subsection 5.

(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 is to 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_min

  • 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 paragraph 4.1; and

  • S_mom,i ≤ 1.

(6) The heeling moment M_heel is to 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 is to 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 on board 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 is to 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 is to 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 is to 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 as amended.

(12) The factor s_i is to 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 as amended;

• (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 will 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-

• H_{j, n, m,} is the least height above the baseline, in metres, within the longitudinal range of x_1(j)...x_2(j+n-1) of the m^th horizontal boundary which is assumed to limit the vertical extent of flooding for the damaged compartments under consideration;

• H_{j, n, m-1,} is the least height above the baseline, in metres, within the longitudinal range of x_1(j)...x_2(j+n-1) of the (m-1)^th horizontal boundary which is assumed to limit the vertical extent of flooding for the damaged compartments under consideration;

• j signifies the aft terminal of the damaged compartments under consideration;

• m represents each horizontal boundary counted upwards from the waterline under consideration;

• d is the draft in question as defined in section 1.3; and

• x₁ and x₂ represent the terminals of the compartment or group of compartments considered in section 4.7.

(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) = 0.8, if (H_m - d) is less than, or equal to 7.8 metres;

• v(H, d) = 0.8 + 0.2 in all other cases,

• where-

• v(H_{j, n, m,} d) is to be taken as 1, if H_m coincides with the uppermost watertight boundary of the ship within the range (x_1(j)…x_2(j+n-1)) and

• v(H_{j, n, 0,} d) is to be taken as 0;

• and in no case is v_m to be taken as less than zero or more than 1.

(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

• ν_m the ν-value calculated in accordance with section 4.7(15);

• s_min the least s-factor for all combinations of damages obtained when the assumed damage extends from the assumed damage height H_m downwards.