## Flotation and stability

A rigid body floating freely on the surface of a fluid has six degrees of freedom, three of translation and three of rotation. For disturbances from a state of equilibrium, the naval architect refers to the movements in the six degrees as follows Fore and aft translation is termed surge. Transverse translation is termed sway. Vertical translation is termed heave. Rotation about a fore and aft axis is termed heel or roll. Rotation about a transverse axis is termed trim or pitch. Rotation about a...

## Determining Hull Efficiency Elements

Having debated in qualitative terms, all the elements involved in propulsion it remains to quantify them. This can be done in a series of model tests. The model is fitted with propellers which are driven through a dynamometer which registers the shaft thrust, torque and revolutions. With the model being towed along the tank at its corresponding speed for the ship speed under study, the propellers are run at a range of revolutions straddling the self-propulsion point for the model. The model...

## E

This is illustrated in Figure 6.5 where AA (AB)2(AC). Having created the motion spectrum, its area can be found and various attributes of the motions deduced as they were for the wave system itself. Thus if mho is the area under the heave spectrum average heave amplitude 1.25 (mho)05 significant heave amplitude 2 (mho)05 average amplitude of highest heaves 2.55 (mho)05 Such values as the significant motion amplitude in the given sea can be used to compare the...

## GG ptgplxw pfgphp PfpVpV

Where p is the density of the water in which the ship is floating and V is the volume of displacement. The effect on the transverse movement of the centre of gravity is to reduce GZ by the amount GGl as in Figure 4.16(b). That is, there is an effective reduction in stability. Since GZ GM sin tp for small angles, the influence of the shift of G to Gx is equivalent to raising G to G2 on the centre line so that GGj GGg tan (p and the righting moment is given W(GM sin < p - GG2 cos (p tan < p)...

## FA dx

If immersed crossr-sectional areas are calculated to a number of waterlines parallel to the design waterline, then the volume up to each can be determined and plotted against draught as in Figure 4.3. The volume corresponding to any given draught T can be picked off, provided the waterline at T is parallel to those used in deriving the curve. A more general method of finding the underwater volume, known as the volume of displacement, is to make use of Bonjean curves. These are curves of...

## Model Experiments

Full scale resistance trials are very expensive. Most of the knowledge on ship resistance has been gained from model experiment. W. Froude was the pioneer of the model experiment method and the towing tank which he opened in Torquay in 1872 was the first of its kind. The tank was in effect a channel about 85 m long, 11m wide and 3 m deep. Over this channel ran a carriage, towed at a uniform speed by an endless rope, and carrying a dynamometer. Models were attached to the carriage through the...

## Vehe0 vihi0 AUfe B0R

Ve(KO) + t (AsO) - A(v,-i e) . _ ---- Bo Gsm < p For very small angles GZ still equates to GM f, so the slope of the GZ curve at the origin equals the metacentric height. That is GM dGZ d< p at < p 0. It is useful in drawing a GZ curve to erect an ordinate at tp 1 rad, equal to the metacentric height, and joining the top of this ordinate to the origin to give the slope of the GZ curve at the origin. The wall-sided formula, derived earlier, can be regarded as a special case of Atwood's...

## Directional Stability And Control

It was seen in an earlier chapter that when a ship at rest in still water is disturbed in the horizontal plane there are no hydrostatic forces to return it to its original position or to increase the movement. The ship is in neutral equilibrium. When a moving ship is disturbed in yaw it is acted upon by hydrodynamic forces which may be stabilizing or destabilizing. If stabilizing, the ship will take up a new steady line of advance but unless some corrective action is applied, by using the...

## Sea keeping

In their broadest sense the terms seakeeping and seaworthiness cover all those features of a vessel which influence its ability to remain at sea in all conditions, for which it has been designed, and carry out its intended mission. They should, therefore, embrace stability, strength, manoeuvrability and endurance as well as the motions of the ship and related phenomena. In this chapter only those aspects of a ship's performance directly attributable to the action of the waves are considered....

## Afc K2 A A05

Thus for dynamic similarity the model propeller must rotate faster than the corresponding ship propeller in the inverse ratio of the square root of the linear dimensions. The thrust power is the product of thrust and velocity and for the same Froude number Correspondingly for torque it can be shown that The rado of torques for geometrically similar propellers at the same advance coefficient and Froude number will be as the fourth power of the linear dimensions. That is Coefficients for...

## Pm X

Assuming water is the medium in which both model and ship are run, the difference in density values will be negligible. For dynamic similarity the pressure must be scaled down in the ratio of the linear dimensions. This can be arranged for the water pressure head but the atmospheric pressure requires special action. The only way in which this can be scaled is to run the model in an enclosed space in which the pressure can be reduced. This can be done by reducing the air pressure over a ship...

## Modes Of Failure

To provide some logical progression through this difficult topic it is instructive to consider first the various ways in which a ship's structure may fail and the possible consequences. Although of rather complex make-up, the ship is essentially an elastic beam floating on the water surface and subject to a range of fluctuating and quasi-steady loads. Those loads will generate bending moments and shear forces which may act over the ship as a whole or be localized. The former will include the...

## Eddy Plate Working Princpal Semi Balance Rudder

In 1957 the International Towing Tank Conference ITTC 5 adopted a model-ship correlation line, based on The term correlation line was used deliberately in recognition of the fact that the extrapolation from model to full scale is not governed solely by the variation in skin friction. Q values from Schoenherr and the ITTC line are compared in Figure 8.8 and Table 8.2. Figure 8.8 Comparison of Schoenherr and ITTC 1957 lines Table 8.2 Comparison of coefficients from Schoenherr and ITTC formulae...

## Floodable Length

Centroid of Centroid of Centroid of volume Vo to volume Vi to lost buoyancy waterline WoLo waterline W, Li waterline is tangent to a line drawn 76 mm 3 inches below the bulkhead deck at side. This line is called the margin line. The jloodable length at any point along the length of the ship is the length, with that point as centre, which can be flooded without immersing any part of the margin line when the ship has no list. Take the ship shown in Figure 4.36 using subscripts 0 and 1 to denote...

## 1 f

The ratio of the buckling stresses in the two cases, for plates of equal thickness and the same stiffener spacing is 4 1 S b 2 -2 Assuming the transversely stiffened panel has a breadth five times its length, this ratio becomes 3.69. Thus the critical buckling stress in a longitudinally stiffened panel is almost four times that of the transversely stiffened panel, demonstrating the advantage of longitudinal stiffening. The above formulae assume initially straight members, axiallv loaded. In...

## F

.Up t model - Om - Os -0175 A selecdon of O and values are presented in Table 8.4. These apply to a standard temperature of 15 C 59 F . The f value is increased or decreased by 4.3 per cent for every 10 C 2.4 per cent for every 10 F the temperature is below or above this value. The two methods above represent two different philosophies for scaling fricuonal resistance. Froude based his method on measurements of the resistance of planks extrapolated to ship-like lengths. Schoenherr and the ITTC...

## The geometry

A ship's hull is three dimensional and, except in a very few cases, is symmetrical about a fore and aft plane. Throughout this book a symmetrical hull form is assumed. The hull shape is defined by its intersection with three sets of mutually orthogonal planes. The horizontal planes are known as waterplanes and the lines of intersection are known as waterlines. The planes parallel to the middle line plane cut the hull in buttodk or bow and buttock lines, the middle line plane itself defining the...

## Simpson S Rules

The trapezoidal rule, using straight lines to replace the actual ship curves, has limitations as to the accuracy achieved. Many naval architectural calculations are carried out using what are known as Simpson's rules. In Simpson's rules the actual curve is represented by a mathematical equation of the form The curve, shown in Figure 3.3, is represented by three equally spaced ordinates yo, yi and y . It is convenient to choose the origin to be at the base of yx to simplify the algebra but the...

## Semi Balanced Rudder

R 0.194 m and diameter of stock 0.388 m In pracdce it would be necessary to take into account the shear force and bending moment on the stock in checking that the strength was adequate. The bending moment and shear forces will depend upon the way the rudder is supported. If astern speeds are high enough the greatest torque can arise then as the rudder is less well balanced for movements astern. The rudder is the most common form of manoeuvring device fitted in ships. Its action in causing the...

## The Screw Propeller

A screw propeller may be regarded as part of a helicoidal surface which, when rotating, 'screws' its way through the water. Consider a line AB, perpendicular to line AA', rotating at uniform angular velocity about AA' and moving along AA' at uniform velocity. Figure 9.2. AB sweeps out a helicoidal surface. The pitch of the surface is the distance travelled along AA' in making one complete revolution. A propeller with a flat face and constant pitch could be regarded as having its face trace out...

## Tchebycheffs Rules

In arriving at Simpson's rules, equally spaced ordinates were used and varying multipliers for the ordinates deduced. The equations concerned can equally well be solved to find the spacing needed for ordinates if the multipliers are to be unity. For simplicity the curve is assumed to be centred upon the origin, x 0, with the ordinates arranged symmetrically about the origin. Thus for an odd number of ordinates the middle one will be at the origin. Rules so derived are known as Tchebycheff rules...

## Superstructures

Superstructures and deckhouses are major discontinuities in the ship girder. They contribute to the longitudinal strength but will not be fully efficient in so doing. They should not be ignored as, although this would 'play safe' in calculating the main hull strength, it would run the risk that the superstructure itself would not be strong enough to take the loads imposed on it at sea. Also they are potential sources of stress concentrations, particularly at their ends. For this reason they...

## Equilibrium Of A Body Floating In Still Water

A body floating freely in still water experiences a downward force acting on it due to gravity. If the body has a mass m, this force will be mg and is known as the weight. Since the body is in equilibrium there must be a force of the same magnitude and in the same line of action as the weight but opposing it. Otherwise the body would move. This opposing force is generated by the hydrostatic pressures which act on the body, Figure 4.1. These act normal to the body's surface and can be resolved...