Regulation 7 - Attained subdivision index A

 The probability of surviving after collision damage to the ship hull is expressed by the index A. Producing an index A requires calculation of various damage scenarios defined by the extent of damage and the initial loading conditions of the ship before damage. Three loading conditions should be considered and the result weighted as follows:

A = 0.4A_s + 0.4A_p + 0.2A_l

where the indices s, p and l represent the three loading conditions and the factor to be multiplied to the index indicates how the index A from each loading condition is weighted.

The method of calculating the A for a loading condition is expressed by the formula:

 i = t

A_c = ∑p_i [v_i s_i ]

i = 1

The index c represents one of the three loading conditions, index i represents each investigated damage or group of damages and t is the number of damages to be investigated to calculate A_c for the particular loading condition.

To obtain a maximum index A for a given subdivision, t has to be equal to T, the total number of damages.

In practice, the damage combinations to be considered are limited either by significantly reduced survivability possibility (i.e., flooding of substantially larger volumes) or by exceeding the maximum possible damage length.

The index A is divided into part factors as follows:

• p_i The p factor is solely dependent on the geometry of the watertight arrangement of the ship.
• v_i The v factor is dependent on the geometry of the watertight arrangement (decks) of the ship and the draught of the initial loading condition. It represents the probability that the spaces above the horizontal subdivision will not be flooded.
• s_i The s factor is dependent on the calculated stability of the ship after damage in a specific initial condition.

Three initial loading conditions should be used for calculating the index A. The loading conditions are defined by their mean draught d, trim and GM.

The mean draught and trim are illustrated in the figure below.

The GM values for the three loading conditions could, as a first attempt, be taken from the intact stability GM limit curve. If the required index R is not obtained, the GM values may be increased, implying that the intact loading conditions from the intact stability book must now meet the GM limit curve from the damage stability calculations derived by linear interpolation between the three GM's.

 The calculations for differing trim should be carried out with the same initial trim for the partial and deepest subdivision draughts. For the light service draught, the actual service trim should be used (refer to the notes to regulation 2, paragraph 11).

Each combination of the index within the formula given in regulation 7.1 should not be less than the requirement given in regulation 6.2. Each partial index A should comply with the requirements of regulation 6.1.

Example:

Based on the GM limiting curves obtained from damage stability calculations of each trim, an envelope curve covering all calculated trim values should be developed.

Calculations covering different trim values should be carried out in steps not exceeding 1% of L_s . The whole range including intermediate trims should be covered by the damage stability calculations. Refer to the example showing an envelope curve obtained from calculations of 0 trim and 1% of L_s .

 In the forward and aft ends of the ship where the sectional breadth is less than the ship's breadth B, transverse damage penetration can extend beyond the centreline bulkhead. This application of the transverse extent of damage is consistent with the methodology to account for the localized statistics which are normalized on the greatest moulded breadth B rather than the partial breadth.

Where corrugated bulkheads are fitted, they may be treated as ordinary stiffened bulkheads as long as the corrugation is of the same order as the stiffening structure.

Pipes and valves directly adjacent to the bulkhead can be considered to be a part of the bulkhead. The same applies for small recesses, drain wells, etc.