CHAPTER III SURFACE VESSELS SECTION 13. BUOYANCY OF A SHIP 1. Forces Acting on a Ship Buoyancy is the ability of a ship to navigate with a designated trim, carrying all loads necessary to execute all combat missions peculiar to the given type of warship. The following forces act on a warship lying dead in the water: 1) The forces represented by the weight of all sections of the ship and objects aboard ship, the resultant of which is the force of the weight of the ship P, applied at the center of gravity Go and acting vertically downward (Fig. 21); 2) Hydrostatic forces of the pressure of the water on the underbody of the ship, the resultant of which is the buoyancy force D, applied at the center of gravity of the submerged volume of the ship and acting vertically upward. The center of gravity of the submerged volume of the ship is called the center of buoyancy Co. In order for the ship to be in equilibrium, its weight must be equal to the force of buoyancy, and the center of gravity and center of buoyancy must lie on the same vertical. If the forces of buoyancy are greater than the weight of the ship, the latter rises, and if less-it submerges. If the center of gravity and the center of buoyancy do not coincide in the fore-and-aft midship plane of the ship, the latter will acquire a trim and incline in the fore-and-aft midship plane until points Go and Co are on the same vertical, after which the ship begins to float in equilibrium, but with a trim. If the center of gravity and the center of buoyancy do not coincide in the fore-and-aft midship plane of the ship, the latter will heel and incline in the fore-and-aft midship plane until points Go and Co coincide along the vertical, after which the ship will float in equilibrium, but with a heel. The volume of water displaced by a floating vessel is called the volume displacement. where 8 = 0.45-0.65 is the coefficient of fullness of displacement—a ratio of the volume of displacement along the designed waterline V to the volume of a parallelepiped constructed on the principal dimensions of the ship: its length L and breadth B along the waterline, in m, and draft T, in m. The values of coefficient 8 for certain types of warships are as follows: cruisers-0.45-0.60; destroyers-0.44-0.53; patrol boats-0.54-0.55; submarines-0.46-0.55. The weight of water displaced by a floating ship is called the weight displacement. D = V[t], (22) where y is the specific weight of the water, t/m3. 2. Summary of Weight of the Hull of a Ship The summary of weight of the hull of a ship is the total weight of all loads comprising the displacement of the ship. The records in which these weights are compiled are called weight of the hull tables. These tables also indicate the locations of the centers of gravity of the weights comprising the summary of weight of the hull and their corresponding moments. There are five characteristic weights of the hull. Light displacement is the displacement of a fully constructed ship with weight meeting approved specifications but without a crew, and also without ammunition and all other expendable materials. Standard displacement is the displacement of a fully constructed and manned ship with weight meeting approved specifications, including the weight of the operational power plant (water in the boilers and systems, fuel and oil in the tanks and machinery) but without reserves of fuel, lubricating oils, tap water and fresh water. Normal displacement (displacement on official trials) is standard displacement plus reserves of fuel, lubricating materials and boiler water up to 50% of reserves, determined by the full load displacement of the ship. Full load displacement is standard displacement plus reserves of fuel, lubricating materials and boiler water in sufficient volume for the assigned range at full and cruising speed. Maximum displacement is full load displacement plus an additional quantity of ammunition, fuel, lubricating materials, feed water and other expendable materials which may be taken aboard ship until all the compartments and spaces designed for storage of these materials are full. SECTION 14. STABILITY OF A SHIP 1. Initial Stability Stability is the ability of a vessel, whose condition of equilibrium has been altered by external forces, to return to this condition after the action of the external forces has discontinued. Stability is classified as initial, i.e., stability with slight deviations from a condition of equilibrium of the ship, and stability with great deviations from a condition of equilibrium of the ship. Inclinations of the ship, at which the volume displacement varies in form, but remains unchanged in magnitude, are called equal-volume inclinations. Waterlines corresponding to these inclinations are also called equal-volume. With successive equal-volume inclinations in one plane, the center of buoyancy C-due to the changing form of the underwater volume-describes a line: path C, the projection of which onto the plane of inclination is called curve Co (Fig. 22, segment CoC1). The metacenter M is called the center of curvature of the curve of the center of buoyancy Co. The metacentric radius is the radius of curvature of curve Co. It can be transverse with athwartship inclinations of the vessel, and longitudinal with longitudinal inclinations of the vessel. The metacentric height-height of the metacenter above the center of gravity of the vessel-is used as a measure of initial stability. Initial stability with athwartship inclinations is characterized by the transverse, or small, metacentric height: h = Zc + r - Zg[m], (23) where Z, and Zg are coordinates of the center of buoyancy and center of gravity of the vessel, m. = = The transverse metacentric height varies for different types of vessels. Thus for cruisers h = 0.9-1.5 m, for destroyers h 0.7-1 m, and for submarines h 0.30-0.45 m. The initial stability of a vessel with any state of its weight load can be approximately determined in the process of operation from the period of free oscillations: where ho, To initial metacentric height, in m, and period of free oscillations of the vessel, in seconds, known from the preceding heeling; h, initial metacentric height, in m, and period of free oscillations, in seconds, determined from swaying test data. If the data of the preceding heeling are unknown, the initial metacentric height is determined from the formula where C - a coefficient, sec2/m; B-breadth of the ship at the design waterline, m; 7 - period of free oscillations from the swaying test, sec. For displacement less than standard in a test, the coefficient C = Cst + 0.1 For displacement greater than standard in a test, the coefficient (25) (26) (27) where Dst D - displacement of the vessel during the test, t; standard displacement of the vessel, t; Cst - coefficient, in sec2/m, for vessels with standard displacement, rec ommended values of which are presented in Table 5. Initial stability with longitudinal inclinations is characterized by a transverse, or large, metacentric height: H = Zc + R Zg[m]. (28) The accuracy in determination of initial metacentric height from the above formulas, in the light to full-load displacement range, is ±10%. 2. Metacentric Initial Stability Formulas If, under the influence of an external heeling moment Mh, a ship deviates slightly from a condition of equilibrium, the force of the weight of the vessel P, remaining applied to the center of gravity Go of the vessel, will be perpendicular to the new actual waterline W1L1. The force of buoyancy D, remaining the same, will be applied at the new location of the center of buoyancy C1, displaced as a result of the altered shape of the underwater volume. This force will also be perpendicular to the new actual waterline W1L1. Thus the force of the weight and the force of buoyancy form a couple (Fig. 23) with arm Gok. The moment of this couple is called the stability moment and is determined by the product of one of these forces and the arm: Me P Gok[tm]. (29) W M Fig. 23. Vessel possessing positive stability. |