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 71Vp, i.e., when the submarine is deeply submerged it acquires residual positive buoyancy

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.

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

If we assume a specific water density 720

=

=

1.0 and volume displacement

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

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

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 y1, varies its 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

in dropping into a layer of water with a higher density, a submarine acquires positive buoyancy, and negative buoyancy when it passes into a layer of water of lower density.

In determining the specific density of sea water, which depends on its temperature and salinity y = (t°,S%), the sea water density table can be used (See Chapter XI, Section 69).

12. Change in Buoyancy as a Function of
Hull Compression at Depth

When a submarine dives, her hull begins to experience pressure from all sides from a water column, which increases with an increase in submergence depth. The water pressure forces acting on the hull decrease volume V, resulting in a loss of buoyancy by the submarine. If the submarine possesses initial volume V, then her volume decreases to H Vp in diving to depth H, and the loss of buoyancy is expressed as follows

Q = YHBV, [T],

p'

(10)

where ẞ is the compression factor per meter of submergence of the submarine, assumed to be 0.000018.

Example: A submarine with pressure hull volume Vp = 1000 m3 dives to depth H = 100 m. The loss of buoyancy from hull compression is

Q = YBVH = 0.000018 1000 • 100y

=

1.8y[T].

Thus, in diving to great depth, a submarine acquires negative buoyancy, due to hull compression.

13. Submergence of a Submarine Under the Influence
of Residual Negative Buoyancy

With negative buoyancy, two forces will act on a diving submarine: force p, equal to the residual negative buoyancy acting vertically downward; and water resistance, acting in a direction opposite from movement of the submarine, i.e., vertically upward, and equal to kSv, where k is a coefficient which depends on the shape of the submarine hull, hull projections and volumes of the superstructure; S is the area of projection of the submarine onto a horizontal plane, and v is the submergence rate of the submarine.

Force kSu increases with an increasing submergence rate, and at a certain moment becomes equal to force p, i.e., p kSv = 0. Hence the maximum submergence rate of the submarine will be

From this moment, movement of the submarine will be uniform.

As the submarine shifts from full buoyancy condition to periscope depth, we can assume a value of 0.06 for coefficient k, and 0.04 with further submergence.

SECTION 6. STABILITY OF A SUBMARINE

1. Stability Conditions

Stability is the ability of a submarine to return to a state of equilibrium once the forces causing deviation from this state are no longer acting.

In the absence of heeling forces, two forces act on the submarine: the force of gravity (weight) P, applied at the center of gravity Go, and the force of buoyancy D, applied at the center of buoyancy Co. Due to equilibrium of the submarine, both of these forces are equal and lie on the same vertical.

When an external pair of forces which do not change the weight and center of gravity of the submarine act on the submarine, the submarine heels at angle (Fig. 3).

The center of gravity of the submarine remains at point Go, and the center of buoyancy Co shifts in the direction of the heel to point C1, due to the change in the shape of the submerged volume.

As a result of the influence of the two forces, which are not in the same plane, a pair of forces with righting moment DGK is formed, which tends to return the submarine to its initial position. In this case the submarine acquires positive stability.

If under the influence of these forces a pair with moment DGK is formed, tending to rotate the submarine in the direction of heel, the submarine acquires negative stability (Fig. 4).

If after inclination of the submarine the center of buoyancy Co is on the same vertical with the center of gravity Go, then the righting moment of the pair of forces will be equal to zero and the submarine will remain in an inclined position, possessing neutral stability (Fig. 5).

With slight inclination of the submarine, the force of buoyancy D intersects the vertical and forms point M, which is called the transverse metacenter. The distance from this point to the center of gravity of the submarine MG is called