CHAPTER 12 SHIP STABILITY AND BUOYANCY

1 CHAPTER 12 ship STABILITY AND BUOYANCYL earning Objectives:Recall the terminology used forship STABILITY ; the laws of physics and trigonometry usedto determine STABILITY and BUOYANCY of a ship ; and theeffects of BUOYANCY , gravity, and weight shifts on the guidance of the damage controlassistant, damage control personnel provide the firstline of defense to ensure your ship is as seaworthy aspossible. Your responsibilities may include preparingdaily draft reports, taking soundings, or perhaps youmay stand watch operating a ballasting this CHAPTER , you will be introduced to the lawsof mathematics and physics used to determine thebuoyancy and STABILITY of a ship . Also, there are variousengineering and mathematical principles that you willbecome familiar with as you study this information on these subjects is provided intheNaval Ships Technical Manual(NSTM), chapter079, volume 1, and inNSTM, CHAPTER 096.

2 You can findadditional information on these subjects inpublications you will find listed in theDamageControlman Advancement OF STABILITYL earning Objectives:Recall the basic functions oftrigonometry, the terminology used for ship STABILITY ,the effects of BUOYANCY and gravity on ship STABILITY , andthe effects of weight shifts on ship comprehend the principles of ship stabilityfully, you must have a basic understanding oftrigonometry and the functions of right speaking, the weight of a ship in the water is pushing straight down, and the seawater that itdisplaces is pushing straight back up. When no otherforces are acting on the ship , all these forces canceleach other out and equilibrium exists.

3 However, whenthe center of gravity moves from directly above thecenter of BUOYANCY , there is an inclining moment. When this occurs, this force is considered to be at rightangles to the forces of gravity and BUOYANCY . Anunderstanding of trigonometry is required tounderstand the effects and results of these is the study of triangles and theinterrelationship of the sides and the angles of atriangle. In determining ship STABILITY , only that part oftrigonometry pertaining to right triangles is is a fixed relationship between the angles of aright triangle and the ratios of the lengths of the sides ofthe triangle. These ratios are known as trigonometricfunctions and have been given the following names:sine, cosine, tangent, cotangent, secant, and three trigonometric functions required for shipstability work are thesine,cosine, andtangent.

4 Figure12-1 shows these trigonometric trigonometry, angles are represented by theGreek letter theta ( ). The sine of an angle ,abbreviated as sin , is the ratio expressed when theside of a right triangle opposite the angle is dividedby the hypotenuse. Figure 12-1 shows thesetrigonometric , referring to figure 12-1:sin = y/r, or the altitude (y) divided by thehypotenuse (r)If the hypotenuse (r) is also the radius of a circle,point P moves along the circumference as the anglechanges in size. As angle increases, side y increasesin length while the length of the hypotenuse (or radius)remains the same. Therefore, the value of the sineincreases as the angle increases.

5 Changes in the valueof the sine corresponding to changes in the size of theangle are shown on the sine curve shown in figure the sine curve, the size of the angle is plottedhorizontally and the value of the sine any angle, the vertical height between thebaseline and the curve is the value of the sine of theangle. This curve shows that the value of the sine at 30 is half of the value of the sine at 90 . At 0 , sin equalszero. At 90 , sin equals cosine is the ratio expressed by dividing theside adjacent to the angle by the , referring to figure 12-1:cos = x divided by r (the adjacent divided bythe hypotenuse)In contrast to the sine, the cosine decreases as theangle becomes larger.

6 This relationship between thevalue of the cosine and the size of the angle is shown bythe cosine curve shown in figure 12-3. At 0 the cosineequals one; at 90 the cosine equals zero; and at 60 thecosine is half the value of the cosine at 0 .TangentThe tangent of the angle is the ratio of the sideopposite the angle to the side adjacent. Again,referring to figure 12-1:Ta n = y divided by x (the side opposite divided by the side adjacent )PRINCIPLES OF PHYSICST here are certain principles of physics that youneed to know in order to have an adequateunderstanding of STABILITY . You should be familiar with12-2 HYPOTENUSE(RADIUS)rRIGHTANGLEPOINTP00000 0(SIDEOPPOSITE)(SIDE ADJACENT TO )yxsin=y=length of the opposite siderlength of the hypotenusecos=x=length of the adjacent siderlength of thethehypotenusetan=y=lengthofopposite sidexlength of the adjacent sideDCf1201 Figure 12-1.

7 Trigonometric (DEGREES)ooooo60 Figure 12-2. Sine (DEGREES)ooooo60 Figure 12-3. Cosine terms asvolume,density,weight,center ofgravity,force, volume of any object is determined by thenumber of cubic feet or cubic units contained in theobject. The underwater volume of a ship is found bydetermining the number of cubic feet in the part of thehull below the density of any material, solid or liquid, isobtained by weighing a unit volume of the example, if you take 1 cubic foot of seawater andweigh it, the weight is 64 pounds or 1/35 of a ton(1 long ton equals 2,240 pounds). Since seawater has adensity of 1/35 ton per cubic foot, 35 cubic feet ofseawater weighs 1 long you know the volume of an object and thedensity of the material, the weight of the object isfound by multiplying the volume by the density.

8 Theformula for this is as follows:W=VxD(weight = volume times density)When an object floats in a liquid, the weight of thevolume of liquid displaced by the object is equal to theweight of the object. Thus, if you know the volume ofthe displaced liquid, the weight of the object is foundby multiplying the volume by the density of the :If a ship displaces 35,000 cubic feet of salt water,the ship weighs 1,000 (weight = volume times density)W = 35,000 cubic feet x 1/35 ton per cubic footW = 1,000 tonsCenter of GravityThe center of gravity (G) is the point at which allthe weights of the unit or system are considered to beconcentrated and have the same effect as that of all thecomponent force is a push or pull.

9 It tends to produce motionor a change in motion. Force is what makes somethingstart to move, speed up, slow down, or keep movingagainst resistance (such as friction). A force may act onan object without being in direct contact with it. Themost common example of this is the pull of are usually expressed in terms ofweight units,such aspounds, 12-4 shows the action of a force on a arrow pointing in the direction of the force is drawnto represent the force. The location and direction of theforce being applied is known as the line of action. If anumber of forces act together on a body, they may beconsidered as a single combined force acting in thesame direction to produce the same overall effect.

10 Inthis manner you can understand that F4 in figure 12-4is the resultant or the sum of the individual forces F1,F2,and you consider the individual forces F1,F2,and F3, or just F4alone, the action of these forces onthe object will move the body in the direction of prevent motion or to keep the body at rest, youmust apply an equal force in the same line of action butin the opposite direction to F4. This new force and F4will cancel each other and there will be no movement;the resultant force is zero. An example of this is a Sailorattempting to push a truck that is too heavy for him tomove. Although the truck does not move, force is stillbeing 12-4. Lines indicating direction of addition to the size of a force and its direction ofaction, the location of the force is important.