Effect of shape and proportions
The most important single factor in cutting down the increased resistance, as well as motions, of ships running in waves appears to be a small fatness ratio; in other words, a small underwater volume compared with the ship length. This slenderness is difficult to work into ships intended to carry cargo but relatively easy for passenger ships. For reduction in the magnitude of ship motions in waves, it is important that the damping forces and moments be as large as practicable. Moderate flare in the above-water sections at bow and stern, large beam compared with draft, and fineness of the underwater sections all help to achieve the result. A deep-sea sailing yacht embodies these characteristics to a high degree.
To keep the ship reasonably dry while undergoing the rolling, pitching, and heaving motions that remain, large freeboard is essential, especially at the bow. To prevent slamming under the bow when it lifts out of water and then drops heavily upon the surface, the forefoot underwater must also be deep.
A good degree of damping is most necessary to avoid deep rolling. If this cannot be achieved by a transverse form suited to the service, such as that of a sailing yacht with a deep fin keel, it is accomplished by adding long fins on each side in the form of roll-resisting or bilge keels. When placed along the lines of flow, these keels add little to the ship resistance in calm water.
Active roll-resisting fins serve to quench the greater part of the roll on a fast ship with a reasonable expenditure of weight, space, and cost. These fins, much shorter than bilge keels but extending several times as far outboard when in use, are rotated mechanically about transverse axes to produce angles of attack and girthwise forces which continually oppose the rolling motion. Since the moments of the roll-resisting forces increase as the square of the ship speed, the active fins are ineffective at low speeds.
Passive roll-resisting tanks of flume or U shape have been extensively installed in ships. In these, the tank dimensions and quantity of water or other liquid are arranged so that the liquid moves from one side of the ship to the other to counteract the rolling motion. Active tanks make use of controllable (and reversible) axial-flow propellers placed in ducts connecting the port and starboard tanks to control the flow.
Considering the vertical accelerations involved, pitching and heaving, or a combination of the two, are particularly objectionable for passenger comfort and safeguarding of cargo. They often necessitate a reduction in speed or a change of course. Some form of passive pitch-resisting fin may be evolved which will accomplish its primary purpose without introducing detrimental features.
Hydrostatic and hydrodynamic loads in service
The naval architect must know the loads imposed upon a ship in all the conditions of its expected service in waves so that a hull structure may be designed to withstand them. Aside from the static distribution of load along the length when the ship is floating at rest in calm water, there are many possible buoyancy distributions in waves for the same loading condition of the ship. Further, the wave action and the ship motion in waves generate dynamic forces which, under certain conditions, may be extremely important. When the bow and stern are on wave crests, with a wave trough between, the ship hull sags or bends downward in the middle. As the middle body reaches a wave crest, with the ends over wave troughs, the ship bends the other way, or “hogs,” and the ends droop because of the greater buoyancy amidships. Waves also produce torsional moments and the hull twists in the seaway, as when the ship is traveling obliquely through waves. Both bending and twisting actions involve shear in the structural members, as when a region that was square in shape under no load takes the shape of a rhombus when deformed. When the ship rolls, racking strains are induced in the hull because the above-water portion wants to continue to roll as the underwater portion starts to roll back the other way. Ship motions also induce inertia forces similar to those felt in elevators when starting or stopping.
It often happens that a part of the hull and an adjacent wave surface, each parallel to and approaching the other, meet with a heavy shocklike impact known as slamming. This can occur if the bow of a ship emerges from the water on a violent up-pitch and drops down upon a rising wave surface. It can also occur if a large wave strikes an overhanging part of the ship, such as the flaring hull under the forward end of the flight deck on an aircraft carrier. The tremendous blow against one end of the hull causes the whole structure to vibrate in an action known as whipping. The strains thus caused may be as great as those encountered in sagging and hogging over large waves.
Other natural loads are those caused by wind and ice. Typhoon and hurricane winds may blow with velocities of 100 knots (185 km per hour) or more. In subfreezing weather the sea spray freezes on the exposed portions of the ship, thereby adding a substantial weight. Icebreakers must be able to withstand the shock of ramming thick solid layers of sea ice and to survive the squeezing action of pack ice.
Many of these loads may be reduced by judicious operation of the ship; for example, by slowing down or heaving to in a storm. Ship structures are designed to withstand most of them, but the exercise of good seamanship significantly lessens their intensity.
Variation of buoyancy and weight along the length of the ship
At a given draft and trim in calm water, the upward buoyancy forces vary from bow to stern in a fixed fashion because each unit length of the ship is supported by a force equal to the weight of water displaced by a transverse section of unit length at that point. When summed up, all the buoyancy forces on the unit lengths equal the total ship weight. The fixed or “hardware” weights of the ship structure, the machinery, the fittings, the equipment, and the fuel and stores, have a somewhat different bow-to-stern distribution when reckoned by the same unit lengths. If the ship is loaded with cargo, some unit lengths weigh less and some more than the water displaced by the immersed volume in those lengths.
Cargo loaded at the ends aggravates this condition and creates an elastic hogging deformation, with the midship portion bent upward and the ends drooping. Cargo loaded in the middle, with the ends empty, creates a sagging of the structure, with the midship portion bent downward. As a first requirement, the ship structure must be strong enough to take care of all the nonuniform weight distributions in calm water during normal loading and unloading. The bending caused by uneven loading, in a tanker carrying liquids and floating in still water, can be sufficient to crack the structure or to break it in two.
When the ship is in waves, the upward buoyancy forces are greatest in way of a crest and least in way of a trough while the ship and cargo weights and the distribution of these weights along the length remain the same. Since two successive waves are rarely alike, it is customary to design the hull structure to withstand the bending moments, in both hogging and sagging, produced by some assumed “standard” series of waves. One such wave has a vertical height in feet, from trough to crest, of 1.1 times the square root of the wavelength in feet. This allows approximately for the observed fact that short waves, the most severe for small boats and ships, have height-to-length or steepness ratios greater than those of long waves. All the "standard" waves have lengths equal to the ship length.
Determination of forces and moments
The maximum forces that a ship is likely to encounter in service, excluding temporarily those due to above-water or underwater explosions, are the weight, inertia, and hydrodynamic forces that act vertically, caused by gravity and by the ship-wave motions. The moments of greatest interest to the designer are the maximum bending moment in the vertical fore-and-aft plane, for both the hogging and the sagging conditions. Slamming forces may act in almost any direction, and they are usually applied at or near the ends of the ship. To predict them it is necessary to make certain assumptions and to use certain approximate formulas not described here.
Prediction of the forces and moments due to above-water or underwater explosions—a possible emergency load for all ship types—requires specialized knowledge and a great deal of experience, much of it of a secret or confidential status. Aside from direct or close hits, the explosive forces produce vertical and lateral bending and whipping, much as do the waves of the sea.
The procedure for determining the design or “standard” wave bending moment is to consider the ship poised and balanced statically on the assumed wave. The wave profile must be adjusted on the ship profile until the total buoyancy forces equal the total weight of the ship, and the centre of gravity is vertically in line with the centre of buoyancy. At any transverse section, the vertical shear is determined by summing up the area under the load curve from one end of the ship to the section in question. By a process known as integration of the moments about a given station, the vertical design bending moment curve is obtained.
Model tests in waves have shown, however, that the dynamic effects of ship pitching and heaving motions in a seaway reduce the bending moment somewhat below that obtained by a quasistatic standard calculation. On the other hand, it appears that the standard wave height is a gross oversimplification of the sea and may not be steep enough.
The solution to the problem has been found by extending the methods described previously in connection with evaluation of ship motions in waves. One can determine the amplitudes of wave-induced bending moment for any ship design in regular waves of various lengths either directly by model tests or by calculations using the equations of motion. Then one can predict a probability distribution of bending moment in several different representative sea states described by their spectra. Knowing the expected frequency of occurrence of each of these sea states in a given service, a long-term probability distribution can be determined. These methods have been applied, for example, in determining the trend of design wave loads for tanker-type hulls as their length has steadily increased. They indicate a leveling off of the design wave height at a constant value when the ship length reaches approximately 1,100 feet (335 metres).
Superposition of calm-water and dynamic wave loads
The final forces and moments which a ship structure is designed to withstand must take account of those imposed by the static loading, such as those due to cargo, fuel, and stores loaded at a pier in port, plus those imposed by wave action and ship motion after the ship puts to sea, including the effects of slamming, lateral bending, and torsion. In fact, under some service conditions, the calm-water bending moment may exceed in magnitude the wave-and-motion moment in a seaway.
