05_Flooding_subdivision

NE224 Spring 2023 Instructor: An Wang 6 Flooding and Subdivision Intact stability Damage stability 6.1 Cause of flooding 1. Hull damage . For example, caused by grounding, collision with other ships/structures, explosion, etc. 2. Downflooding . For example, water flows through openings in the deck in heavy weather. 6.2 Scenarios of flooding 1. The top of the flooded compartment remains waterproof and is below the waterline. There is no free surface inside the flooded compartment. The flooding water can be treated as a weight loaded to the ship. 2. The flooding water inside the compartment is not connected to the outside water and there is a free surface inside the flooded compartment. For example, water flows downward into the hold from the weather deck, or a bilged and resealed compartment with flooding water still remaining inside. The water can be treated as a liquid weight loaded to the ship and the liquid weight has a free surface. 3. (Most common) The top of the flooded compartment is above the waterline. The flooding water inside the compartment is connected to the outside water. The water surfaces inside and outside are at the same level. In this case, it is more convenient to treat the displacement of the ship as unchanged. Part of the flooded volume (lost buoyancy) is shifted to occupy another volume (regained buoyancy), causing the shift of the center of buoyancy of the ship. Typically, the area and moment of inertia of the waterplane are reduced and the draft of the ship increases. The third scenario is further discussed in the following. 1

NE224 Spring 2023 Instructor: An Wang 6.3 Definitions Figure 6.1: Process of flooding. 1) Active buoyancy : the buoyant volume ∇ when the intact ship is floating at stable equilibrium at even keel. 2) Reserve buoyancy : the internal watertight volume of the compartments above the waterline and up to the bulkhead deck. 3) Lost buoyancy : after the ship regained equilibrium, the volume of the bilged com- partment up to the original intact waterline (W 0 L 0 ). 4) Regained buoyancy : the buoyant volume between intact waterline W 0 L 0 and the flooded waterline W ′ L ′ outside of the flooded compartment. 5) Subdivision bulkhead : bulkheads that divide the ship into separate watertight compartments. Without subdivision bulkhead, if there is a hole on the hull below waterline, the ship must sink. 2

NE224 Spring 2023 Instructor: An Wang 1. Effect of flooding on draft and freeboard Flooding will increase draft and reduce freeboard. (Exception: before damage, the flooded compartment was filled with liquid to a level above the final equilibrium waterline. In this case, the liquid is replaced with flooding water and the draft may decrease, depending on how much liquid is in the compartment and the density of the liquid. ) Foundering: the loss of a ship due to complete loss of reserve buoyancy without heeling and with positive stability. For example, the flooded waterline reaches the bulkhead deck and the reserve buoyancy is used up. 2. Effect of flooding on stability Flooding will reduce area, longitudinal and transverse moment of inertia of the water plane ( A w , I L and I T , respectively). As a result, the vessel’s TPI, BM T and BM L are reduced. Recall: GM = KM − KG = KB + BM − KG . When flooding increases draft: KB increases, to some extent offset the decrease in BM . Therefore, KM may not decrease due to flooding, depending on the location and geometry of the flooded compartment as well as the geometry of the hull. Most of the time, when flooded, the reduction in I T is significant so that the transverse stability GM T will decrease. For example, when the flooded compartment is at the widest part of the ship, the loss of GM T can be significant. If GM T becomes negative, the ship will have an angle of loll and not be able to remain upright. Note: even if the flooded compartment is symmetric about the ship’s longitudinal or transverse center of gravity, the flooding can still cause the ship to trim or heel or even capsize, due to the reduced stability. 3. Effect of flooding on trim If the flooded compartment is toward forward, the ship will trim by head; if flooded compartment is toward aft, the ship will trim by stern. Think: how do the center of gravity and center of buoyancy shift to regain equilibrium? Plunge : the ship dives into water upended due to significant loss in longitudinal stability as a result of reduced longitudinal moment of inertia of waterplane. This can happen even- tually as water gradually floods through openings on the deck, if the trimmed ship cannot regain equilibrium before the deck immerses. 4

NE224 Spring 2023 Instructor: An Wang 4. Effect of flooding on heel If flooded compartment is toward starboard, the ship will heel toward starboard; if flooded compartment is toward port, the ship will heel toward port. During the process of flooding, the heel caused by flooding, combined with the reduced transverse stability can further increase the possibility of capsizing. 6.5 Limiting flooding by subdivision Considerations for limiting the effect of flooding: 1) Number of transverse bulkheads. Too few: The flooding of one compartment may cause significant loss of buoyancy, stability. Too many: Smaller cargo space and access, not economic. Increase of chance of damaging multiple bulkheads at the same time. 2) Strength of the bulkheads to sustain pressure. 3) Specific requirements (location, spacing and strength) of subdivision for different types of compartments. 6.6 Calculation of condition after damage 6.6.1 Permeability of flooded spaces Volume permeability ( µ ) : The ratio of the volume of flooding water ( v w ) that enters a compartment to the molded volume of the compartment ( v c ) µ = v w v c (6.1) Approximated values of volume permeability for typical compartment: Space and Contents Permeability, Percent Empty or void compartment 95 Dry cargos or stores 60 Accommodation spaces 95 Machinery spaces 85 Container holds (containers flooded) 70 RO/RO holds (wheeled vehicles) 90 Barge ship holds (barges flooded) 76 Barge ship holds (barges intact) 30 5

NE224 Spring 2023 Instructor: An Wang and all of the other ship characteristics as flooding progresses. The added weight method requires more calculation, because one does not know the final trim line after damage so iteration is needed. One first guess a final trim line to calculate a weight and centroid of the flooding water that enters the ship. 6.6.4 Computer methods 6.7 Floodable length Margin line : The margin line is an imaginary line above which the hypothetical ship ends. The hypothetical ship is assumed to only have hull and subdivision bulkhead but with no deck (an open-top “canoe”). The location of the margin line varies depending on ship configurations and regulations, for example, no less than 3 in below the upper surface of the bulkhead deck at side. Floodable length : The floodable length at any point in the length of the ship is the maximum portion of the ship’s length, having its center at the point in question, that can be symmetrically flooded at a given permeability, without immersing the margin line. Figure 6.3: Floodable length definitions. Note: Use the isosceles triangle in figure 6.3 to determine the floodable length at a particular location for a given permeability. The angle of the side of the triangle with horizontal is arctan 2. The floodable length only describes the survivability of the ship subject to sinkage and trim due to flooding, but it does not consider heel. Use floodable length curves to test/determine the compartment length (location of bulk- heads). If the vertex of the triangle falls below the floodable length curve of the corresponding 7

NE224 Spring 2023 Instructor: An Wang permeability of this compartment, the ship will not plunge to sink if this compartment is flooded. One compartment ship: The first tier vertices all fall below the floodable length curves of corresponding permeability of the compartments. The ship can survive the damage to one compartment. Two-compartment ship: The second tier vertices also fall below the floodable length curves of corresponding permeability of the compartments. The ship can survive damage anywhere in its length, including on a subdivision bulkhead, unless the opening in the hull is so long that it damages two bulkheads and causes three compartments to be flooded. Reference: How is floodable length calculated, see Principles of Naval Architecture , Lewis, 1988, Vol. 1, p. 152. 6.8 Subdivision standards and criteria Typical standards require the ship designer to assume a prescribed extent of damage (length, penetration, vertical extent, etc.), location of damage (between bulkheads or on bulkheads) and acceptable condition of flotation and stability after the damage (location of margin line, maximum angle of list, minimum GM , etc.). Three typical approaches: Integer compartmentation: One-compartment or two-compartment ship? Regula- tions require that the ship must survive the flooding of an integer number of compartments simultaneously. May permit a ship to have different compartmentation standards for differ- ent portions of the ship, based on the knowledge that some parts of of the ship are statistically more likely to be damaged than others. Factor of subdivision: A factor of subdivision is a number equal to or less than one that multiplies the floodable length to define the permissible length of a ship’s compartments. The assumption of this concept is that multiplying floodable length by a factor smaller than one, i.e., smaller spacing between bulkheads, always improves the survivability after the damage. Cons: 1) decreasing the spacing between bulkhead may increase the probability of dam- age to multiple bulkheads, increasing the chance to flooding two or more compartments. 2) the probability of containing the length of damage within one compartment decreases as bulkheads get closer. 8