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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 Dati

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 Deri

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


Db Dk




Depending upon hull design, the reserve buoyancy of submarines varies by 15-30%.

7. Residual Buoyancy

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 and the weight force Pp, i.e.,

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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 = 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.

MQ = Ps · XGp [Tm).


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 Vk, which with constant weight of the submarine disturbs equilibrium, and the submarine either rises, if Dk >P, or submerges deeper, if Dk <P.

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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 7 Vk, then proceeding into water with weight density Y1, with the same volume displacement Vk, it will be equal to

Di = Y Vk:


The difference between the forces of buoyancy

Di - Dk = (01 - y) Vk


This means that in order to maintain the trim of a submarine along the full buoyancy waterline, its weight P must vary by (Y1 - ) 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 71 - 1.025 T/m3. The volume displacement of the submarine Vk

1430 m3.

amount of ballast which must be taken aboard in order to return the submarine to its previous full buoyancy condition will be


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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.

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If the buoyancy of a submerged submarine at the surface of the water is equal to Vp,

then if the submarine is submerged to depth H m buoyancy becomes 71 Vp, i.e., when the submarine is deeply submerged it acquires residual positive buoyancy

Q = (y1 - y) Vp

H 10


100,000 · TóYV IT).

Here Vp is the volume of the submarine pressure hull with hull projections, without taking the main ballast tanks into account. The latter are in free communication with the sea water and, consequently, the acquired residual positive buoyancy in their volume is dissipated by the increased weight of the water in the tanks themsleves.

10. Change in Weight Density of the Water as a

Function of Variation in Temperature


The weight density of water varies with changes in temperature. Fresh water has its highest weight density at +4°C. With a change in temperature in either direction, the weight density of fresh water decreases. With a change in temperature from +20° to +10°, the weight density of fresh water increases 0.015% on the average per degree, and with a subsequent change in temperature from +10° to +4°, it increases 0.005%.

The specific density of distilled water as a function of temperature is shown in Table 3.

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Example: A submarine was submerged in water at a temperature of +20°C and a specific gravity of y20, then dropped into a layer of water with a temperature of +6°C.

Due to the temperature decrease, the specific density of the water is increased, and will be

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If we assume a specific water density 720 1.0 and volume displacement

= 1000 m3, then, as a result of the temperature drop from +20° to +6°C, the submarine acquires a positive buoyance of


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When a submerged submarine passes from water of one salinity with specific density y into water of another salinity with specific density 71, the buoyancy of the submarine varies

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In certain areas of the sea the specific density of the water can vary sharply. Such a phenomenon is encountered wherever there are underwater currents, and also along the banks of river mouths, where large masses of fresh water do not immediately mix with the surrounding sea water, and retain their specific density in a certain sector, sharply diverging from the specific density of the sea water.

A submarine trimmed in water with specific density y, having dropped in a submerged condition into a layer of water with a specific density of 71, varies its

a buoyancy. The variation in buoyancy can be considerable, and makes it impossible for the submarine to descend below this layer without acquiring a trim by the head and increasing her speed. If these measures do not suffice, additional ballast may also have to be taken on.

Sharp increases in the specific density of the water can be used to anchor the submarine under water without a way on. A water layer varying significantly in salinity or temperature from surrounding layers is called a thermal layer. Thus

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