Regulation 7-2
Calculation of the Factor “ s i ”
of Merchant Shipping (Safety Convention) Regulations
[S 892/2023 wef 01/01/2024] ( a ) 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 Regulation: “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 equalization (if any) until final equilibrium has been reached. ( a ) (i) 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 — “S intermediate,i ” is the probability to survive all intermediate flooding stages until the final equilibrium stage, and is calculated in accordance with paragraph ( b ); “S final,i ” is the probability to survive in the final equilibrium stage of flooding. It is calculated in accordance with paragraph ( c ); “S mom,i ” is the probability to survive heeling moments, and is calculated in accordance with paragraph ( d ). ( b ) For passenger ships, and cargo ships fitted with cross-flooding devices, the factor “S intermediate,i ” is 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 m; “Range” is not to be taken as more than 7°; and “S intermediate,i ”= 0, if the intermediate heel angle exceeds 15° for passenger ships and 30° for cargo ships. For cargo ships not fitted with cross‑flooding devices the factor “S intermediate,i ” is taken as unity, except if the Director considers that the stability in intermediate stages of flooding may be insufficient, it should require further investigation thereof. For passenger and cargo ships, where cross‑flooding devices are fitted, the time for equalisation shall not exceed 10 min. [S 872/2019 wef 01/01/2020] ( c ) The factor “S final,i ” shall be obtained from the formula — where — “GZ max ” is not to be taken as more than “TGZ max ”; “Range” is not to be taken as more than “TRange”; “TGZ max ” = 0.20 m, for ro‑ro passenger ships each damage case that involves a ro‑ro space; “TGZ max ” = 0.12 m, otherwise; “TRange” = 20º, for ro‑ro passenger ships each damage case that involves a ro‑ro space; “TRange” = 16º, otherwise; “K” = 1 if θ e ≤ θ min “K” = 0 if θ e ≥ θ max where — θ min is 7° for passenger ships and 25° for cargo ships; and θ max is 15° for passenger ships and 30° for cargo ships. [S 872/2019 wef 01/01/2020] ( d ) The factor “S mom,i ” is applicable only to passenger ships (for cargo ships “S mom,i ” shall be taken as unity) and shall be calculated at the final equilibrium from the formula — where — “Displacement” is the intact displacement at the respective draught (“d s ”, “d p ” or “d l ”); “M heel ” is the maximum assumed heeling moment as calculated in accordance with paragraph ( d )(i); and “S mom,i ” ≤ 1. ( d ) (i) The heeling moment “M heel ” is to be calculated as follows: M heel = maximum (M passenger or M wind or M survivalcraft ). [S 872/2019 wef 01/01/2020] ( d ) (i)(1)“M passenger ” is the maximum assumed heeling moment resulting from movement of passengers, and is to be obtained as follows: 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 breadth of the ship as defined in Regulation 2( h ). 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. In doing so, a weight of 75 kg per passenger is to be assumed. [S 872/2019 wef 01/01/2020] (2) “M wind ” is the maximum assumed wind moment acting in a damage situation: where — “P” = 120 N/m 2 ; “A” = projected lateral area above waterline; “Z” = distance from centre of lateral projected area above waterline to T/2; and “T” = respective draught (“d s ”, “d p ” or “d l ”). [S 872/2019 wef 01/01/2020] (3) “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. 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; (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. [S 872/2019 wef 01/01/2020] ( e ) Unsymmetrical flooding is to be kept to a minimum consistent with the efficient arrangements. 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 of passenger ships and the freeboard deck of cargo ships. These fittings together with their controls shall be acceptable to the Director * . Suitable information concerning the use of equalisation devices shall be supplied to the master of the ship. * Reference is made to the Revised recommendation on a standard method for evaluating cross-flooding arrangements, adopted by the Organisation by resolution MSC.362(92), as may be amended. [S 872/2019 wef 01/01/2020] ( e ) (i) Tanks and compartments taking part in such equalization shall 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. (ii) The factor “s i ” is to be taken as zero in those cases where the final waterline, taking into account sinkage, heel and trim, immerses —
for cargo ships, 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; (2) any part of the bulkhead deck in passenger ships considered a horizontal evacuation route for compliance with Chapter II-2; and (3) for passenger ships subject to the provisions of Regulation 1( a )(i)(1) and constructed before 1 January 2024, 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. [S 892/2023 wef 01/01/2024] (iii) 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 —
immersion of any vertical escape hatch in the bulkhead deck of passenger ships and the freeboard deck of cargo ships intended for compliance with Chapter II-2; (2) 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 of passenger ships and the freeboard deck of cargo ships become inaccessible or inoperable; (3) immersion of any part of piping or ventilation ducts located within the assumed extent of damage and carried through a watertight boundary if this can lead to the progressive flooding of compartments not assumed as flooded; and (4) for passenger ships constructed on or after 1 January 2024, immersion of 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. [S 892/2023 wef 01/01/2024] (iv) However, 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 equalization in additional flooding phases. (v) Except as provided in paragraph ( e )(iii)(1), openings closed by means of watertight manhole covers and flush scuttles, remotely operated sliding watertight doors, side scuttles of the non-opening type as well as watertight access doors and watertight hatch covers required to be kept closed during navigation in accordance with Regulations 22 to 24 need not be considered. [S 892/2023 wef 01/01/2024] ( f ) 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 sub-paragraph ( a )(i) by the reduction factor “v m ” according to sub-paragraph ( f )(i), which represents the probability that the spaces above the horizontal subdivision will not be flooded. ( f ) (i) The factor “v m ” shall be obtained from the formula — 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 draught in question as defined in Regulation 2; and “x 1 ” and “x 2 ” represent the terminals of the compartment or group of compartments considered in Regulation 7-1. ( f ) (i)(1) The factors “v(H j, n, m , d)” and “v(H j, n, m-1 , d)” shall be obtained from the formulae — if (H m – d) is less than, or equal to, 7.8m; 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 (x1 ( j ) ...x2 (j+n-1) ), and “v(H j, n, 0 , d)” is to be taken as 0. In no case is “v m ” to be taken as less than zero or more than 1. (ii) In general, each contribution “dA” to the index “A” in the case of horizontal subdivisions is obtained from the formula — dA = p i • [v 1 • s min1 + (v 2 – v 1 ) • s min2 + •••• +(1 – v m-1 ) • s min m ] where –– v m = the “v”-value calculated in accordance with sub-paragraph ( f )(i); 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. [S 686/2008 wef 01/01/2009]