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Submarine:
Submarines are vehicles designed to operate principally at a considerable depth of water.
Most applications to date are warfare activities. Submarines have also some civil applications like oceanographic researches, pipe laying & servicing well heads at sea bed.
1. Hull:
1.1. Introduction
The aim of this design study is to produce a shape with the following features:
1. Minimum resistance within all other design constraints, thus increasing cruising range, top speed and reducing fuel consumption.
2. Minimum flow noise especially over the forward sonar and other sensors.
3. A flexible interior giving most deck space for a given volume.
1.2. Criteria for Optimum Shape of a Submarine
Gertler, in 1950 [10], reported the results of resistance experiments on a systematic series of twenty four mathematically related streamlined bodies of revolution, showing how the resistance of these bodies at deep submergence varies with changes in five selected geometrical parameters. These geometrical parameters were the fineness ratio, prismatic coefficient, nose radius, tail radius and the position of the maximum section. Before this work was undertaken there was no systematic data on the resistance of streamlined forms deeply submerged in a fluid These test results formed the basis for the choice of the shape of the USS Albacore [25], whose construction was authorized in 1951. This experimental vessel was the forerunner of all successful US Navy submarines such as Barbel and Skipjack
1.3. Cross-Section
To withstand the high pressures on the hull at depth, the most efficient structural shape with the lowest stresses is one of circular cross-section.
Departures from absolute circularity have to be minimized as discussed by Capt. H. E. Saunders [4], otherwise early failures can result. The circle has the lowest wetted surface for a given contained volume so this is an advantage for underwater resistance.
1.4. Length-to-Diameter Ratio
The ratio of length-to-diameter bears a strong effect on the total resistance. The two main portions of the underwater resistance of the bare hull are due to pressure drag(sometimes called form drag) and skin friction.
The pressure drag is created by the streamlines on the rear of the body being displaced from the geometric surface by the thickening boundary layer. Consequently the rise in pressure near the tail of the body as the streamlines widen, is not as great as would occur without a boundary layer. This imbalance between nose and tail produces a nett pressure force on the submarine creating a drag force.
Skin friction drag acts tangentially at the surface and is proportional to the wetted surface. The more wetted surface the greater the skin friction. Therefore if the displaced volume of the submarine is contained in a long thin shape, then the skin friction is greater than for a shorter, beamier shape of the same volume which has less wetted surface.
The combined resistance shows a minimum at about L/D of 6 to 7
1.5. Surface Roughness
The main factor, apart from surface area, which affects the skin friction resistance, is the roughness of the surface. It is important that designers limit the effects of surface openings, raised edges, recessed joins (shutters), lateral arrays and other features which cause added resistance
1.6. Prismatic Coefficient
CP Prismatic Coefficient = Displaced Volume Midship Area×Waterline Length
1.7. Limitations on Draft
It should be possible to increase the floating draft of a submarine to greater than that of Collins, which is nominally 7.0 metres, and still be able to navigate the important harbours where it docks and berths.
The weight of any new vessel needs to be established early in the design
. Hence the floating draft can be established from the displaced volume required to support this weight added to all the other loadings. Arentzen and Mandel [6] suggest that 36 feet(10.98 metres) is the upper practical limit for the diameter of a military submarine which would have a draft of 30 feet (9.14 metres).
1.8. Diving Depth (Critical Pressure)
Timoshenko [5, pp186-188] discusses the buckling of reinforcing rings for submarines and shows that the second moment of area formed by the cross-section of the ring, which may include part of the skin, needs to be maintained in the same ratio with the cube of the diameter in order to maintain the same critical collapse pressure. To reach the same diving depth with the same factor of safety as Collins, the larger diameter vessel will need stronger rings with deeper webs. This is a penalty for increasing the diameter.
1.9. Number of Decks
An important consequence of an increase in diameter involves the number of decks. Collins with diameter of 7.8 m contains three decks. The floor-to-floor height of the’tween-decks is about 2.15 m. It is quite possible to have two tween decks with this headroom and almost the same headroom as Collins for the upper and lowest decks. The hull diameter then becomes 9.6 m
2. Stability:
Figure 5-6. Change of center of buoyancy and metacenter during submergence
The three points, B, G, and M, are much closer together than is the case with surface ships. When a submarine is submerged, these significant points are arranged much differently.
The center of gravity of the submarine, G, remains fixed slightly below the centerline of the boat while B and M approach each other, B rising and passing G, until at complete submergence B and M are at a common point. These changes are shown diagrammatically in Figure 5-6.
On the surface the three points, B, M, and G, are in the same relative positions as for surface ships. As the ballast tanks fill, the displacement becomes less with the consequent rising of B and lowering of M. There is a point during submergence or surfacing when B coincides with G and GM becomes zero or perhaps a negative quantity. During a normal dive, this point is passed so quickly that there is no time for the boat to take a list. When the ballast tanks are fully flooded, B rises to the normal center of buoyancy of the pressure hull, and stability is regained with G below B.
Just why these centers change so radically may be made more readily apparent by an illustration with rectangular sections. The diagrams in Figure 5-7 represent a rectangular closed chamber, so weighted at G that it will sink in water. The area surrounding it at the sides and bottom represents air chambers.
At A, the vessel is floating with all water excluded from the tank surrounding the chamber. The center of gravity is at G and the center of buoyancy, B, is found by intersecting diagonals of the displacement.
At B, water has been admitted to the lower section of the tank. Using the diagonals as before, it is seen that the center of buoyancy, B, is now coincident with G and the unit is unstable.
At C, the surrounding tank is flooded and the unit is submerged. The center of buoyancy is at B2, the intersection of the diagonals of the displaced water. The unit is stable, the center of buoyancy and the center of gravity are in the same vertical line. Any rotational movement about the center of buoyancy B2 immediately sets up a restoring moment arm.
When surfacing, with the water ballast being ejected comparatively slowly by the low-pressure blowers, GM may become negative and a list may occur. As a corrective measure, if a list should occur, certain main ballast tanks are provided with separate low-pressure blow lines for the port and starboard sections. Lever-operated, list control valves are installed so that air to the tanks on the high side may be restricted and more air delivered to the low side.
2.1. Transverse stability
The stability of any vessel on the surface depends upon two things: 1) the position of the center of gravity, and 2) the shape of the vessel. The shape above the waterline, the freeboard, and the shape below the waterline all affect stability.
It is an axiom that high freeboard and flare assure good righting arms and increase stability, and low freeboard and "tumble home," or inward slope, give small righting arms and less stability. The diagrams in Figure 5-8 show why this is true.
Diagram A represents a cylindrical vessel with its center of gravity at the center of the body and so weighted that it floats on its centerline. Its center of buoyancy is at the center of gravity of the displaced water.
It is at once apparent that this vessel is not in stable equilibrium. G and B will remain in the same position regardless of rotation of the body. As no righting arms are set up, the vessel will not return to its original position.
Diagram B represents a vessel of equal volume and the same waterline. Its center of gravity is at the center of volume, and the center of buoyancy is at the center of gravity of the displaced water. When this vessel is inclined about its center of gravity, the effect of change of shape is noticeable. The volume of displaced water at the left of G is decreased and the displacement at the right is increased. The center of buoyancy moves to the right, the metacenter, M, is above G, and the force coupled B1G, tends to right the vessel.
In diagram C the vessel is flared from the waterline and its freeboard increased. When this vessel is inclined, the added displacement of the flare is added to that resulting from the shape of the underwater section, and the center of buoyancy shifts about four times as far, raising the metacenter and providing a stronger righting arm.