the transverse metacentric height h, or pa, which characterizes the stability of the submarine. Distance p from the transverse metacenter M to the center of buoyancy Co is called the transverse metacentric radius. The distance between the center of gravity Go and the center of buoyancy Co is designated by the letter a. If point M lies above the center of gravity Co, the submarine possesses positive stability (Fig. 6). If point M lies below the center of gravity, it possesses negative stability (Fig. 4). If the submarine is inclined, the righting moment M, is equal to M, = D(pa) sin 0, (12) where p α 0 transverse metacentric radius; height of the center of gravity of the submarine above the center of buoyancy; angle of heel. This expression is called the metacentric transverse stability formula. The value of the transverse metacentric height pa for various classes of submarines is not the same and varies within the limits 0.25-0.50 m. 3. Change in Transverse Stability Due to a With a load displacement p1 along the vertical to height h1, the weight of the submarine and her load waterline remain unchanged. The metacenter also remains the same. The center of gravity of the submarine, on the basis of the theory of displacement of the center of gravity, shifts in the direction of load displacement: Since stability is determined by the distance between the metacenter and the center of gravity, with load displacement along the vertical the new metacentric height MG1 = p-a GoG1. (14) In displacing the load upward from the initial position, the change in stability GoG is customarily designated with a “-” sign, and with a “+” sign when it is displaced downward. From this expression it is evident that with upward load displacement the stability of the submarine decreases, and increases with downward displacement. 4. Change in Transverse Stability in Diving Ballasting the tanks produces a change in weight of the submarine, its volume of displacement, and the actual waterline area, which in turn displaces three points: center of gravity Go, center of buoyancy Co, and metacenter Mo Since the stability of a submarine is determined by the relative position of points Go, Co and Mo, their position will change until the submarine is at full submergence. When a submarine dives, the following changes occur in the position of points Go, Co and Mo: 1) with an increase in the submerged volume, the center of buoyancy Co will be displaced upward; 2) with the main ballast tanks full, the center of gravity Go will first drop, then rise; 3) metacentric radius p will decrease due to a decrease in the actual waterline area, but metacenter Mo will approach the center of buoyancy; with full submergence, metacenter M will coincide with the center of buoyancy Co (Fig. 7). The stability of a submerged submarine determines the relative position of points Go and Co. Let us examine two positions of the center of gravity Go and center of buoyancy Co a) The center of gravity is above the center of buoyancy (Fig. 8). When the submarine is inclined, the buoyancy force and weight of the submarine create a pair of forces tending to capsize the submarine. In this case, the submarine possesses negative stability. b) If the center of gravity is below the center of buoyancy, the buoyancy forces and weight of the submarine create a pair of forces tending to restore the submarine to its initial position. In this case, the submarine possesses positive stability (Fig. 9). Fig. 7. Graph depicting change in the position of the center of gravity Go, center of buoyancy Co and metacenter Mo with submergence of a submarine; 1) Distance from the baseline; 2) Draft. Fig. 8. Position of the center of gravity Go and center of buoy. ancy Co when the submerged submarine possesses negative stability. D Co Go Fig. 9. Position of the center of gravity Go and center The righting moment in the submerged condition M, = Da sin 0, (15) buoyancy force, equal to the weight of the submarine; distance between the center of gravity Go and the center of buoyancy Co. 5. Change in Transverse Stability in Grounding and Docking In full buoyancy condition, a submarine possesses waterline WoLo. In grounding, part of its volume of displacement emerges from the water, and a new waterline W1L1 (Fig. 10) appears. In this case, the following forces will act on the submarine: P D weight of the submarine, applied at the center of gravity Go; P1 - weight of water in volume WOLOW1L1, applied at point A; When the submarine is inclined at angle 0, two pairs of forces will be created: P, D and R, P1. The moment of the pair of forces P and D is the righting moment: The moment of the pair of forces R and P1 is the heeling moment of the The resultant moment is equal to the algebraic sum of the moments M = D(p − a) sin ( P1AH sin 0 = De-a-AH) sin (17) 0. (18) It is evident from this expression that the initial metacentric height of the Pl submarine p a decreases by the amount AH, numerically equal to the amount of displacement of the center of gravity of the submarine with displacement of load P1 along the vertical from the point of tangency of the keel to the center of gravity of the volume WOLOW1L1 emerging from the water. When a submarine docks, a phenomenon similar to grounding occurs, i.e., in this case the metacentric height likewise decreases by the same amount. SECTION 7. WATERTIGHT INTEGRITY OF SUBMARINES 1. Surface Watertight Integrity For submarines, watertight integrity is classified as surface or submerged. Surface watertight integrity is the ability of a submarine to remain afloat with positive stability when the airtightness of the pressure and false hulls is disturbed due to partial loss of reserve buoyancy. Submerged watertight integrity is the ability of a submarine to remain at depths not exceeding the maximum operating depth, shipping water into the pressure hull, to navigate submerged and rise to the surface of the sea. Surface watertight integrity of a submarine is usually maintained with flooding of one compartment from the adjoining main ballast tanks from one side, and, in rare instances, with flooding of two adjoining compartments. Flooding of one compartment of the pressure hull and adjoining side tanks while the submarine is operating in a surface condition is tantamount to taking on cargo from one side (at the bow or stern, on the port or starboard side), the only difference being that in event of heavy damage large masses of water are shipped, and, as a rule, with large trim and heeling moments. This complicates determination of the stability, trim, heel and forward and aft draft of the submarine. With a small reserve buoyancy and with trim, the actual waterline undergoes significant changes, expressed by a decrease in transverse and longitudinal stability. The primary means for maintenance of watertight integrity are: 1) high-pressure air; 2) utilizing speed in a submerged condition; 3) damage control gear; 4) bilge pumps. |