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1. The initial metacentric height, after correction for the free surface effects of liquids in tanks, shall not be less than 0.70 m.
2. The angle of heel due to the shift of grain shall not be greater then 12° or the angle at which the deck edge is immersed, whichever is the lesser.
3. In the statical stability diagram, the net of residual area between the heeling arm curve and the righting arm curve up to the angle of heel of maximum difference between the ordinates of the two curves, or 40° or the angle of flooding (Θf), whichever is the least, shall in all conditions of loading be not less than 0.120 metre-radians.
A damage stability analysis serves the purpose to provide proof of the damage stability standard required for the respective ship type. At present, two different calculation methods, the deterministic concept and the probabilistic concept are applied.
SCOPE OF ANALYSIS AND DOCUMENTATION ON BOARD
1. The scope of subdivision and damage stability analysis is determined by the required damage stability standard and aims at providing the ships master with clear intact stability requirements. In general, this is achieved by determining KG-respective GM-limit curves, containing the admissible stability values for the draught range to be covered.
2. Within the scope of the analysis thus defined, all potential or necessary damage conditions will be determined, taking into account the damage stability criteria, in order to obtain the required damage stability standard. Depending on the type and size of ship, this may involve a considerable amount of analyses.
3. Referring to SOLAS chapter regulation 19, the necessity to provide the crew with the relevant information regarding the subdivision of the ship is expressed, therefore plans should be provided and permanently exhibited for the guidance of the officer in charge. These plans should clearly show for each deck and hold the boundaries of the watertight compartments, the openings therein with means of closure and position of any controls thereof, and the arrangements for the correction of any list due to flooding. In addition, Damage Control Booklets containing the aforementioned information should be available.
1. The scope of subdivision and damage stability analysis is determined by the required damage stability standard and aims at providing the ships master with clear intact stability requirements. In general, this is achieved by determining KG-respective GM-limit curves, containing the admissible stability values for the draught range to be covered.
2. Within the scope of the analysis thus defined, all potential or necessary damage conditions will be determined, taking into account the damage stability criteria, in order to obtain the required damage stability standard. Depending on the type and size of ship, this may involve a considerable amount of analyses.
3. Referring to SOLAS chapter regulation 19, the necessity to provide the crew with the relevant information regarding the subdivision of the ship is expressed, therefore plans should be provided and permanently exhibited for the guidance of the officer in charge. These plans should clearly show for each deck and hold the boundaries of the watertight compartments, the openings therein with means of closure and position of any controls thereof, and the arrangements for the correction of any list due to flooding. In addition, Damage Control Booklets containing the aforementioned information should be available.
For the checking of the input data, the following should be submitted:
.1 main dimensions;
.2 lines plan, plotted or numerically;
.3 hydrostatic data and cross curves of stability (including drawing of the buoyant hull);
.4 definition of sub-compartments with moulded volumes, centres of gravity and permeability;
.5 layout plan (watertight integrity plan) for the sub-compartments with all internal and external opening points including their connected subcompartments, and particulars used in measuring the spaces, such as general arrangement plan and tank plan. The subdivision limits, longitudinal, transverse and vertical, should be included;
.6 light service condition;
.7 load line draught;
.8 coordinates of opening points with their level of tightness (e.g., weathertight, unprotected);
.9 watertight door location with pressure calculation;
.10 side contour and wind profile;
.11 cross and down flooding devices and the calculations thereof according to resolution MSC.245(83) with information about diameter, valves, pipe lengths and coordinates of inlet/outlet;
.12 pipes in damaged area when the destruction of these pipes
Subdivision length (Ls) Different examples of Ls showing the buoyant hull and the reserve buoyancy are provided in the figures below. The limiting deck for the reserve buoyancy may be partially watertight. The maximum possible vertical extent of damage above the baseline is ds + l2,5 m.
Light service draught (dl) The light service draught (dl) represents the lower draught limit of the minimum required GM (or maximum allowable KG) curve. It corresponds, in general, to the ballast arrival condition with l0 % consumables for cargo ships. For passenger ships, it corresponds, in general, to the arrival condition with l0 % consumables, a full complement of passengers and crew and their effects, and ballast as necessary for stability and trim. The l0 % arrival condition is not necessarily the specific condition that should be used for all ships, but represents, in general, a suitable lower limit for all loading conditions. This is understood to not include docking conditions or other non-voyage conditions.
.1 subdivision length Ls;
.2 initial draughts and the corresponding GM-values;
.3 required subdivision index R; and
.4 attained subdivision index A with a summary table for all contributions for all damaged zones.
2 Results for each damage case which contributes to the index A:
.1 draught, trim, heel, GM in damaged condition;
.2 dimension of the damage with probabilistic values p, v and r;
.3 righting lever curve (including GZmax and range) with factor of survivability s;
.4 critical weathertight and unprotected openings with their angle of immersion; and
.5 details of sub-compartments with amount of in-flooded water/lost buoyancy with their centres of gravity.
The attained subdivision index A is determined by a formula for the entire probability as the sum of the products for each compartment or group of compartments of the probability that a space is flooded, multiplied by the probability that the ship will not capsize or sink due to flooding of the considered space. In other words, the general formula for the attained index can be given in the form:
Subscript i represents the damage zone (group of compartments) under consideration within the watertight subdivision of the ship. The subdivision is viewed in the longitudinal direction, starting with the aftmost zone/compartment.
The value of pi represents the probability that only the zone i under consideration will be flooded, disregarding any horizontal subdivision, but taking transverse subdivision into account. Longitudinal subdivision within the zone will result in additional flooding scenarios, each with its own probability of occurrence.
The value of si represents the probability of survival after flooding the zone i under consideration.
In case of cargo ships greater than 100 m in length Ls: ;
In case of passenger ships: ; were N=N1+2N2
N1 number of persons for whom lifeboats are provided;
N2 number of persons (including officers and crew) the ship is permitted to carry in excess of N1
1.Longitudinal extent: 1/3 or 14.5 m (whichever is the less).
2. Transverse extent measured inboard of ship side at right angles to the centre line at the level of the deepest subdivision load line: 1/5 of the ship breadth B or 11.5 m (whichever is the less).
3. Vertical extent: from the base line upwards without limit.
Model testing Empirical methods Computational techniques
expression for definition of force of full resistance to body movement in the water looks like
Where R - full force of resistance of water to body movement;
ζ - dimensionless factor of resistance;
ρ - density of environment;
Ω - the characteristic area of a body;
υ - relative speed of movement of a body
In this expression
where Re Reinoldls number;
Fr Froudes number.
expression Re-u, Fr-w we can describe as f(Re, Fr) than we have a conclusion
Use f(Re, Fr) = ζ, 2 = Ω, if к = 0,5, than
.
Froude considered, that by comparison of the ship and its model from the point of view of wave dynamics of a condition in two geometrically similar cases will be identical, if length of ship Ls and its models Lм are among themselves in such relation, as lengths cased them of waves. And consequently, according to the law of mechanical similarity, and its models Vм it is possible to express the relation of speeds of ship Vк the equation. In other words, speeds of the ship and its model are proportional to square roots from their linear sizes.
Froude number Fmr = Fsr
Fmr = =
v- velocity l - length g - gravity
Vm/ = Vs/
Problems that take place during vessels motion are slamming whipping springing propeller racing sloshing deck wetnesses surge sway heave roll pitch yaw overkill.
Slamming is the impact of the bottom structure of a ship onto the sea surface. It is mainly observed while sailing in waves, when the bow raises from the water and subsequently impacts on it.
Whipping is a hull vibration with a fundamental two-noded frequency. It can produce stresses similar in magnitude to the quasi-static wave-bending stresses. It also can produce very high local damage
Springing is global vertical resonant hull girder vibration due to oscillating wave loads along the hull of the ship
Sloshing creates an impact force between the free surface of the fluid and the tank structure
If a ship's bow is pushed into the deep water the wave crest may come down on the forecastle deck this is called deck wetness.
Speed reduction in waves occur because of two factors. These are known as voluntary and involuntary speed loss.
Voluntary speed loss is due to a decision, by the captain, to reduce speed in order to reduce the motions, slams, deck wetness etc. to within acceptable limits. This may also necessitate a change of course.
Involuntary speed loss arises from the fact that a vessel travelling through waves will have a greater resistance due to its motions. Also it is likely that the propeller will be less efficient due to the motions and oscillations of the onset stream. These effects may reduce the vessel's speed by around two to three knots but this may be sufficient to result in substantial financial losses for a merchant ship.
The transverse strength loads act on transverse members causing structural distortion of the outer shell, bottom structure, ballast tanks, etc. There are two impact loads classified as transverse strength loads: slamming and sloshing. Slamming may be categorized as a transverse strength load as well as a longitudinal one. It means the impact force as the shell plating hits the water surface severely. Therefore, it generates not only a longitudinal load but also a load affecting the transverse strength simultaneously. Many ships are damaged by slamming resulting in denting of shell plating, in particular the bottom forward shell plating. If a ship's bow is pushed into the deep water the wave crest may come down on the forecastle deck. This is called "deck wetness by green water" and may cause damage of the ship's structure and deck machinery. In case if propeller accelerates more than it is constructed for due to water less in case of waves it may concern a serious damage of a shaft and propeller in its own.