Submarine Theory

Above buoyancy

Surface buoyancy of a submarine, similar to the buoyancy of a surface ship, is characterized by a buoyancy margin . That is, the ratio of waterproof volumes above the waterline (OHL) to the entire waterproof volume is expressed as a percentage.

For example, if the total submarine volume is 3000 m³, and the surface part is 600 m³, then the buoyancy margin:

W = 600/3000 * 100 = 20%

The same attitude can be expressed in displacement . For this example, in distilled water (1 m³ = 1 t), the displacement will be

D _n = 3000 - 600 = 2400 t,

and the displacement of its total volume D _p = 3000 tons. Then

W = (Dp - Dn) / D _p * 100

Submarine buoyancy

Underwater buoyancy is fundamentally different from surface. To completely submerge a boat in water, you need to bring its weight to the weight of the water displaced by its full volume. In other words, to repay the buoyancy margin of up to 0% by taking in additional cargo ( ballast ), in practice, outboard water. From the point of view of physics, we can also assume that the boat reduces its volume, letting the surrounding sea into the hull . In the theory of submarines, the first approach was adopted - ballast water is considered the property of the boat, that is, cargo. And they say that the surface displacement is less than the underwater. In our example - 2400/3000 tons. As you can see, the buoyancy reserve can be expressed as the ratio of surface and underwater displacements.

However, if you take more cargo than a fully submerged submarine weighs (to create negative buoyancy ), it will not swim in the underwater position, and if it sinks, it will continue to sink until it reaches the ground or collapses. Therefore, it is vital that the theoretical underwater buoyancy is precisely neutral - 0%. For a surface ship, this boundary state is equated to loss of buoyancy, for a submarine it is an everyday norm.

The buoyancy is obviously affected by the weight of the submerged body and the density of water. Since in practice neither one nor the other remains constant (the boat has residual buoyancy ), maintaining neutral buoyancy of submarines under water requires corrections. They are made by pumping / receiving ballast, which is called a submarine sign , or stabilization of depth.

In practice, the reception of ballast requires time and energy. Therefore, the golden rule of a surface ship: “the larger the stock, the better” is contrary to technical requirements. Structural stock of buoyancy trying to limit. Typically, it is 8-30% for submarines (depending on the project), compared with 50-60% or more for surface ships. A smaller stock contradicts the requirements of unsinkability, a larger one - the speed of immersion / ascent and the restriction on structural dimensions.

Surface stability

The principles of surface stability of submarines are also similar to the stability of a surface ship. In the same way distinguish between static and dynamic stability.

The submarine on an even keel is also in an unstable position equilibrium . ^{[2] [3]} The center of magnitude (CV, C ) is located under the center of gravity (CT, G ). When the roll Θ or trim Ψ appears, the CV shifts, the support force γV forms with the force of gravity P the shoulder of the regenerating moment m _in .

A feature of the transverse stability of a submarine is that its hull , for reasons of strength, has a circular cross section. Therefore, with an increase in heel, changes in the area of ​​the existing waterline are insignificant (that is, the stability of the form does not increase). The healing moment with an increase in the roll varies little. Small and initial metacentric height h .

Both transverse and longitudinal surface stability of submarines are affected by the presence of a large amount of liquid cargo, usually with free surfaces , in auxiliary ballast and special tanks. All of them reduce the margin of dynamic stability. Unlike a surface ship, where free surfaces are tried to allow as little as possible, the submarine, by its very structure, is forced to have them.

For this reason, the margin of dynamic surface stability of a submarine is less than that of a surface ship. That is, submarines, as a rule, are more roll on the surface.

Underwater stability

Underwater stability of submarines is fundamentally different from surface. Under water, the submerged volume is generally constant. CV is not shifted. Therefore, a restoring moment as a surface type cannot occur. In the underwater position, stable balance is required. That is, the DH should be below the CV. Then any roll or trim creates a couple of forces that straighten the boat. The stability of the form is absent, there is only the stability of weight . However, any shift in the DH affects the position of the boat in the water — landing .

Especially a boat under water is sensitive to longitudinal forces causing trim. The overturning moments arising at the same time ( m _cr ), in the absence of stability of the form, often exceed the rectifying ones, and are dangerous for the boat. Archimedean forces are not enough to compensate, and artificial intervention is required. It is carried out by the longitudinal displacement of the load, called trim . ^[four]

Immersion stability (ascent)

Stability during immersion (ascent) is a special case in which the main parameters that determine stability are variable. There is a transition from unstable balance (surface position) to stable (underwater). It is accompanied by a temporary decrease in stability. The height of the CV (Z _c ) above the main plane grows with depth, the height of the CT (Z _g ) first decreases, then grows, the height of the metacentre (Z _m , not to be confused with the metacentric height) grows, then decreases, and grows again.

Their combined influence is described by the buoyancy and initial stability diagram of the submarine. Two singular points of the diagram: I — coincidence of CV and CT. The restoring moment is determined only by the moment of stability of the form. II - leaving under water a durable case . The metacentre merges with the CV, the metacentric height is minimal.

During immersion and ascent, there are more than ever (except for cases of damage) free surfaces - in the tanks of the main ballast. Therefore, the margin of dynamic stability of the submarine is minimal.

Surface and underwater propulsion of submarines are very different. For a submarine, as for a surface ship, the dependences of resistance on speed are fair. Resistance is proportional to the square of the speed:

X = f * V ²

where V is the speed, f is the proportionality coefficient.

The required power is proportional to the cube of the rotational speed of the screw ( screw characteristic ):

N _e = m * w³

where m is the coefficient, w is the rotation frequency.

Free surface movement is characterized by the presence of wave drag ( X _in ), form resistance ( X _f , see the coefficient of form resistance ) and friction resistance ( X _t ). At full speed in the above-water position, the wave resistance reaches 50-60% of the total. Underwater propulsion is characterized in that wave impedance is absent X _at = 0 (starting from a depth equal to half the length of the boat).

Thus, it is impossible to create a case that satisfies both modes. Moreover, a satisfactory compromise is also impossible. Therefore, the shape of the case is optimized for a more characteristic mode.

Historically, two periods have been observed. The first, when the underwater and surface engines were completely separate. The submarines were mainly diesel-electric and spent most of the time in the water position. The submarines of this time had a superstructure and a light hull with contours connecting the boat to the surface ship. The surface speed of these submarines was, in a typical case, greater than the underwater.

With the advent of the snorkel (RDP), the boundary between the underwater and surface engines is blurred, and with the advent of nuclear energy, boats get a single engine. The surface position is not characteristic. Therefore, the shape of the hull is fully optimized for underwater travel. Since the 1960s, it has been close to perfect hydrodynamic - teardrop-shaped, with a relative elongation of L / B = 6 ÷ 7. The shape resistance is minimized. The main share (85 - 90%) is the friction resistance. Such boats are capable of developing greater speed under water than on the surface.

Surface roll

The submarine is characterized mainly by surface rolling. In the surface position to the submarine, all considerations applicable to the roll of the surface ship are applicable. Although the boat, like the surface ship, has all 6 degrees of freedom , the most significant impact on it is on-board and keel pitching .

The difference in the pitching of the submarine is a large amplitude . According to the operating experience, it can reach Θ = 60 °, with a wave of 5 - 6 points. ^[five]

Scuba

Submarine submarine is only noticeable only in the near-surface layer. It affects the operation of submarines using retractable devices, primarily RPDs, and the conditions for launching missiles from an underwater position. Thus, we are talking about diving depths from 10 m ( periscopic depth) to 45 m (starting depth).

The fillability of the RPD head significantly affects the ventilation of the submarine and imposes requirements on equipment, depending on the flow of air. But for the PL theory, the pitching at the periscope depth is similar to the surface.

Beginning in the 1960s , research was carried out on the surface rolling of submarines. ^[6] The results are as follows:

• rocking at the surface significantly affects the orientation of the rockets when leaving the water
• pitching at the starting depth affects the orientation of the rockets when exiting mines / torpedo tubes, but slightly
• starting from a depth of 100 m, the effect of pitching is absent

• Bubnov, Ivan Grigorievich
• Krylov, Alexey Nikolaevich

• podlodka.info// Fundamentals of the theory of submarines