CHAPTER II SUBMARINES SECTION 5. BUOYANCY OF A SUBMARINE 1. Trim of a Submarine The trim of a submarine is her position relative to a calm water surface. The surface position of a submarine is characterized by the parameters of her trim overall: draft (7), heel (0) and trim (V). If the fore-and-aft line and the plane of the midship frame are vertical, the submarine is upright and on an even keel. In this case, the waterline is parallel to the reference plane, and its position is determined by a single draft T, whereby == 0. If the fore-and-aft line and the plane of the midship frame are inclined, the submarine lies with a heel and trim. The trim of a surfaced submarine is determined by the draft marks, located on the outer hull of the submarine on each side at the bow and stern, usually equidistant from the midship frame. 2. Center of Gravity and Center of Buoyancy Buoyancy is the ability of a submarine to navigate on the surface along the designated waterline, and submerged at depths not exceeding the maximum operating depth, while carrying all loads according to specification. A submerged submarine is subjected to pressure from all sides. The pressure forces are perpendicular to the pressure hull surface and proportional to the submarine's submergence depth H. All horizontal components of the normal forces tend to compress the submarine, whereas the parallel vertical components create a resultant upward force D, equal to the weight of the water in the volume of the submerged body. Force D is called the force of buoyancy, and its point of application Co is called the center of buoyancy (Fig. 2). Moreover, the force of gravity P (weight of the submarine), acting vertically downward, also acts on the submarine. The force of buoyancy D and force of gravity P lie on the same vertical. The resultant of these two forces is equal to their difference and is in the direction of the greater force. In the first case, when the weight P of the submarine is greater than the force of buoyancy D, their resultant is downward. The submarine will dive. In the second case, when the weight P of the submarine is equal to the force of buoyancy D, the resultant is equal to zero and the submarine will maintain equilibrium. In the third case, when the weight P of the submarine is less than the force of buoyancy D, their resultant is upward and the submarine begins to climb. It will continue to climb while forces P and D are unequal, and will stop only after part of the volume of the submarine extends above the surface of the water and the force of buoyancy decreases to the weight of the submarine, i.e., when force D becomes equal to force P. The center of gravity Go changes its position only if there is a change in the weight of the load or if it is displaced from one position to another along the length or breadth of the submarine. The center of buoyancy Co is the center of gravity of the volume of water displaced by the submerged section of the submarine. Its position varies depending on the shape and size of the submerged volume of the submarine. 3. Weight and Volume Displacement The submerged volume of a submarine V (in m3) serves as a measure of buoyancy and is called volume displacement. The weight of the water in volume Vis called weight displacement D. Weight Displacement where y-specific gravity of the water, depending upon salinity, temperature and pressure, T/m3. V - volume displacement of the submarine, m3. 4. Conditions of a Submarine Depending upon the amount of ballast in the main and auxiliary ballast tanks, a submarine may have the following four conditions: 1) Full buoyancy-surface condition of a trimmed submarine with a full buoyancy control tank and unfilled main ballast tanks. Such a condition of the submarine corresponds to full buoyancy displacements: volume displacement Vk and weight displacement Dk. The waterline determining this displacement is called the full buoyancy waterline; 2) Diving trim-surface condition of a trimmed submarine with full main ballast tanks, except for the midship group, and with an unfilled buoyancy control tank. Such a condition of the submarine corresponds to diving trim displacement Dat; 3) Draft-surface condition of a trimmed submarine with a full buoyancy control tank and a large fuel reserve, located in the fuel ballast tanks. Such a condition of the submarine corresponds to displacement with fuel in transshipment Dtr; 4) Submerged-condition of a trimmed submarine navigating at depths from periscope to maximum operating depth with a full buoyancy control tank. Such a condition corresponds to the submerged displacements: volume displacement V, and weight displacement Dp. 5. Summary of Weight of Hull The summary of weight of hull of a submarine is the total weight of all loads on the submarine. This includes not only the weight of individual loads Pi, but also their disposition aboard the submarine, defined by the coordinates of their centers of gravity Xpi, Ypi, and Zpi The generalizing characteristics of the summary of weight of hull are the weight of the submarine P and the coordinates of its center of gravity Xg, Yg, and Zg. All of the loads aboard a submarine are classified as constant, variable, deficient or transient. In the process of navigating a submarine after weighing, when her summary of weight of hull is reduced to normal, personnel must cope only with a change in summary of weight of hull due to variable loads. 6. Reserve Buoyancy Reserve buoyancy is the impenetrable volume of a submarine above full buoyancy waterline, or the volume of all the main ballast tanks. Reserve buoyancy can also be considered the load which the submarine can take on above its normal load prior to full submergence. Ordinarily, reserve buoyancy is expressed in percentages of full buoyancy displacement RB Db 100%. (3) Depending upon hull design, the reserve buoyancy of submarines varies by 15-30%. 7. Residual Buoyancy and Residual buoyancy Q is a force acting along the vertical and equal, in the submerged condition, to the difference between the forces of buoyancy Dp the weight force P, i.e., In navigating, it is difficult to achieve a condition in which the residual buoyancy is equal to zero, although they strive for this in the process of stopped trim. Actually, it ordinarily lies within the limits ±0.0002 Pp. In practice, as we know, there are three possible cases: Pp > Dp, Pp Pp = Dp' and Pp Dp. Therefore, it is said that a submarine possesses residual negative buoyancy, residual positive buoyancy, or residual neutral buoyancy. A change in residual buoyancy, resulting from a change in the weight of a submarine, produces a longitudinal trim moment. If the residual buoyancy of a submarine is caused by a change in only the force of buoyancy, the longitudinal trim moment will not act on the submarine. 8. Effect of Weight Density of Water on the Volume Displacement of a Submarine The weight density of water, even within the confines of a single sea, can vary considerably. The specific gravities of the waters of various seas and oceans are presented in Table 1. Variations in the weight density of water affect the force of buoyancy Dk = YVk, which with constant weight of the submarine disturbs equilibrium, and the submarine either rises, if Dk >P, or submerges deeper, if Dk <P. In order to maintain a constant volume displacement of the submarine Vk or trim along a full buoyancy waterline, the weight of the submarine must vary by an amount equal to the variation in the force of buoyancy. If, in water with weight density y, force of buoyancy Dk = yVk, then proceeding into water with weight density 71, with the same volume displacement Vk, it will be equal to This means that in order to maintain the trim of a submarine along the full buoyancy waterline, its weight P must vary by (Y1 - Y)Vk· Example: A submarine in full buoyancy condition passes from water with a weight density of y = 1.015 T/m3 into water with a density of 1 - 1.025 T/m3. The volume displacement of the submarine Vk = 1430 m3. The amount of ballast which must be taken aboard in order to return the submarine to its previous full buoyancy condition will be With increasing depth, the weight gravity of water y increases, on the average, 0.005% for every 10 m of depth, as is evident from Table 2. |