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 loadline 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 loadline 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

(2) The factor p(x1, x2) is to be calculated according to the following formulae-

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_n is to 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)