CHAPTER 12 SHIP STAILITY AND UOYANCY Learning Objectives: Recall the terminlgy used fr ship stability; the laws f physics and trignmetry used t determine stability and buyancy f a ship; and the effects f buyancy, gravity, and weight shifts n ship stability. Under the guidance f the damage cntrl assistant, damage cntrl persnnel prvide the first line f defense t ensure yur ship is as seawrthy as pssible. Yur respnsibilities may include preparing daily draft reprts, taking sundings, r perhaps yu may stand watch perating a ballasting cnsle. In this chapter, yu will be intrduced t the laws f mathematics and physics used t determine the buyancy and stability f a ship. Als, there are varius engineering and mathematical principles that yu will becme familiar with as yu study this chapter. Detailed infrmatin n these subjects is prvided in the Naval Ships Technical Manual (NSTM), chapter 079, vlume 1, and in NSTM, chapter 096. Yu can find additinal infrmatin n these subjects in publicatins yu will find listed in the Damage Cntrlman Advancement Handbk. PRINCIPLES OF STAILITY Learning Objectives: Recall the basic functins f trignmetry, the terminlgy used fr ship stability, the effects f buyancy and gravity n ship stability, and the effects f weight shifts n ship stability. T cmprehend the principles f ship stability fully, yu must have a basic understanding f trignmetry and the functins f right triangles. Generally speaking, the weight f a ship in the water is pushing straight dwn, and the seawater that it displaces is pushing straight back up. When n ther frces are acting n the ship, all these frces cancel each ther ut and equilibrium exists. Hwever, when the center f gravity mves frm directly abve the center f buyancy, there is an inclining mment. When this ccurs, this frce is cnsidered t be at right angles t the frces f gravity and buyancy. An understanding f trignmetry is required t understand the effects and results f these actins. TRIGONOMETRY Trignmetry is the study f triangles and the interrelatinship f the sides and the angles f a triangle. In determining ship stability, nly that part f trignmetry pertaining t right triangles is used. There is a fixed relatinship between the angles f a right triangle and the ratis f the lengths f the sides f the triangle. These ratis are knwn as trignmetric functins and have been given the fllwing names: sine, csine, tangent, ctangent, secant, and csecant. The three trignmetric functins required fr ship stability wrk are the sine, csine, and tangent. Figure 12-1 shws these trignmetric relatins. Sine In trignmetry, angles are represented by the Greek letter theta (θ). The sine f an angle θ, abbreviated as sin θ, is the rati expressed when the side f a right triangle ppsite the angle θ is divided by the hyptenuse. Figure 12-1 shws these trignmetric relatins. Therefre, referring t figure 12-1: sin θ = y/r, r the altitude (y) divided by the hyptenuse (r) If the hyptenuse (r) is als the radius f a circle, pint P mves alng the circumference as the angle changes in size. As angle θ increases, side y increases in length while the length f the hyptenuse (r radius) remains the same. Therefre, the value f the sine increases as the angle increases. Changes in the value f the sine crrespnding t changes in the size f the angle are shwn n the sine curve shwn in figure 12-2. On the sine curve, the size f the angle is pltted hrizntally and the value f the sine vertically. At any angle, the vertical height between the baseline and the curve is the value f the sine f the angle. This curve shws that the value f the sine at 30 is half f the value f the sine at 90. At 0, sin θ equals zer. At 90, sin θ equals ne. 12-1
POINT P HYPOTENUSE (RADIUS) r RIGHT 0 ANGLE x (SIDE ADJACENT TO 0 ) y (SIDE OPPOSITE 0 ) sin 0 = y length f the ppsite side = r length f the hyptenuse cs 0 = x length f the adjacent side = r length f the hyptenuse 0 the tan = y lengthf ppsite side = x length f the adjacent side Figure 12-1. Trignmetric relatinships. DCf1201 1 1 0.5 0.5 0 0 60 90 180 270 360 cs 0 (DEGREES) 0 0 60 90 180 270 360 cs 0 (DEGREES) -1 Figure 12-2. Sine curve. DCf1203-1 Figure 12-3. Csine curve. DCf1203 Csine Tangent The csine is the rati expressed by dividing the side adjacent t the angle θ by the hyptenuse. Therefre, referring t figure 12-1: cs θ = x divided by r (the adjacent divided by the hyptenuse) In cntrast t the sine, the csine decreases as the angle θ becmes larger. This relatinship between the value f the csine and the size f the angle is shwn by the csine curve shwn in figure 12-3. At 0 the csine equals ne; at 90 the csine equals zer; and at 60 the csine is half the value f the csine at 0. The tangent f the angle θ is the rati f the side ppsite the angle θ t the side adjacent. Again, referring t figure 12-1: Tan θ = y divided by x (the side ppsite θ divided by the side adjacent θ) PRINCIPLES OF PHYSICS There are certain principles f physics that yu need t knw in rder t have an adequate understanding f stability. Yu shuld be familiar with 12-2
such terms as vlume, density, weight, center f gravity, frce, and mments. Vlume The vlume f any bject is determined by the number f cubic feet r cubic units cntained in the bject. The underwater vlume f a ship is fund by determining the number f cubic feet in the part f the hull belw the waterline. Density The density f any material, slid r liquid, is btained by weighing a unit vlume f the material. Fr example, if yu take 1 cubic ft f seawater and weigh it, the weight is 64 punds r 1/35 f a tn (1 lng tn equals 2,240 punds). Since seawater has a density f 1/35 tn per cubic ft, 35 cubic feet f seawater weighs 1 lng tn. Weight If yu knw the vlume f an bject and the density f the material, the weight f the bject is fund by multiplying the vlume by the density. The frmula fr this is as fllws: W=VxD(weight = vlume times density) When an bject flats in a liquid, the weight f the vlume f liquid displaced by the bject is equal t the weight f the bject. Thus, if yu knw the vlume f the displaced liquid, the weight f the bject is fund by multiplying the vlume by the density f the liquid. Example: If a ship displaces 35,000 cubic feet f salt water, the ship weighs 1,000 tns. W=VxD(weight = vlume times density) W = 35,000 cubic feet x 1/35 tn per cubic ft W = 1,000 tns Center f Gravity The center f gravity (G) is the pint at which all the weights f the unit r system are cnsidered t be cncentrated and have the same effect as that f all the cmpnent parts. Frce A frce is a push r pull. It tends t prduce mtin r a change in mtin. Frce is what makes smething start t mve, speed up, slw dwn, r keep mving against resistance (such as frictin). A frce may act n an bject withut being in direct cntact with it. The mst cmmn example f this is the pull f gravity. Frces are usually expressed in terms f weight units, such as punds, tns. runces. Figure 12-4 shws the actin f a frce n a bdy. An arrw pinting in the directin f the frce is drawn t represent the frce. The lcatin and directin f the frce being applied is knwn as the line f actin. If a number f frces act tgether n a bdy, they may be cnsidered as a single cmbined frce acting in the same directin t prduce the same verall effect. In this manner yu can understand that F4 in figure 12-4 is the resultant r the sum f the individual frces F 1, F 2, and F 3. F 1 F F 2 F 3 DCf1204 Figure 12-4. Lines indicating directin f frce. Whether yu cnsider the individual frces F 1,F 2, and F 3, r just F 4 alne, the actin f these frces n the bject will mve the bdy in the directin f the frce. T prevent mtin r t keep the bdy at rest, yu must apply an equal frce in the same line f actin but in the ppsite directin t F 4. This new frce and F 4 will cancel each ther and there will be n mvement; the resultant frce is zer. An example f this is a Sailr attempting t push a truck that is t heavy fr him t mve. Althugh the truck des nt mve, frce is still being exerted. F 4 12-3
Mments In additin t the size f a frce and its directin f actin, the lcatin f the frce is imprtant. Fr example, if tw persns f the same weight sit n ppsite ends f a seesaw, equally distant frm the supprt (fig. 12-5), the seesaw will balance. Hwever, if ne persn mves, the seesaw will n lnger remain balanced. The persn farthest away frm the supprt will mve dwn because the effect f the frce f his/her weight is greater. c DCf1206 Figure 12-6. Diagram t illustrate the mment f frce. A special case f mments ccurs when tw equal and ppsite frces nt in the same line rtate a bdy. This system f tw frces, as shwn in figure 12-7, is termed a COUPLE. The mment f the cuple is the prduct f ne f the frces times the distance between them (fig. 12-8). d F DCf1205 Figure 12-5. The balanced seesaw. The effect f the lcatin f a frce is knwn as the MOMENT OF FORCE. It is equal t the frce multiplied by the distance frm an axis abut which yu want t find its effect. The mment f a frce is the tendency f the frce t prduce rtatin r t mve the bject arund an axis. Since the frce is expressed in terms f weight units, such as tns r punds, and the mment is frce times distance, the units fr mment are expressed as ft-tns, ft-punds, r inch-unces. In figure 12-6 the mment f frce (F) abut the axis at pint a is F times d; d being called the mment arm. The mment f a frce can be measured abut any pint r axis; hwever, the mment differs accrding t the length f the mment arm. It shuld be nted that the mment f a frce tends t prduce rtary mtin. In figure 12-6, fr example, the frce F prduces a clckwise rtatin. If, at the same time, an equal and ppsite frce prduces a cunterclckwise rtatin, there will be n rtatin; and the bdy is in equilibrium. DCf1207 Figure 12-7. Equal and ppsite frces acting n a bdy (nt in the same line). Calculatin f the mment f the cuple, as shwn in figure 12-8, is as fllws: The mment f the cuple =Fxd Therefre, the mment f the cuple is 50 feet times 12 punds that equals 600 ft-punds. F = 50 LS. 12 FT F = 50 LS. DCf1208 Figure 12-8. Diagram t shw calculatin f the mment f a cuple. 12-4
In ne sense, a ship may be cnsidered as a system f weights. If the ship is undamaged and flating in calm water, the weights are balanced and the ship is stable. Hwever, the mvement f weight n the ship causes a change in the lcatin f the ship s center f gravity, and thereby affects the stability f the ship. Figure 12-9 shws hw an INCLINING MOMENT is prduced when a weight is mved utbard frm the centerline f the ship. If the bject weighing 20 tns is mved 20 feet utbard frm the centerline, the inclining mment will be equal t 400 ft-tns (F x d, r 20 x 20). mment, use the ship s baseline, r keel, as the axis. Figure 12-11 shws the calculatin f the vertical mment f a 5-inch gun n the main deck f a ship. The gun weighs 15 tns and is lcated 40 feet abve the keel. The vertical mment is thus 15 x 40, r 600 ft-tns. 15 TONS 40 FEET d ORIGINAL POSITION w NEW POSITION Figure 12-11. Vertical mment. ASE LINE DCf1211 UOYANCY VERSUS GRAVITY DIRECTION OF MOMENT DCf1209 Figure 12-9. Inclining mment prduced by mving a weight utbard. Figure 12-10 shws hw a frward (r aft) mvement f weight prduces a TRIMMING MOMENT. Let s assume that a 20-tn weight is mved 50 feet frward; the trimming mment prduced is 20 x 50, r 1,000 ft-tns. ORIGINAL POSITION t NEW POSITION DIRECTION OF MOMENT DCf1210 It is als pssible t calculate the VERTICAL MOMENT f any part f the ship s structure r f any weight carried n bard. In calculating a vertical w Figure 12-10. Trimming mment. uyancy may be defined as the ability f an bject t flat. If an bject f a given vlume is placed under water and the weight f this bject is GREATER than the weight f an equal vlume f water, the bject will sink. It sinks because the FORCE that buys it up is less than the weight f the bject. Hwever, if the weight f the bject is LESS than the weight f an equal vlume f water, the bject will rise. The bject rises because the FORCE that buys it up is greater than the weight f the bject; it will cntinue t rise until it is partly abve the surface f the water. In this psitin the bject will flat at such a depth that the submerged part f the bject displaces a vlume f water EQUAL t the weight f the bject. As an example, take the cube f steel shwn in figure 12-12. It is slid and measures 1 ft by 1 ft by 1 ft. If yu drp the steel cube int a bdy f water, the steel cube will sink because it weighs mre than a cubic ft f water. ut if yu hammer this cube f steel int a flat plate 8 feet by 8 feet, bend the edges up 1 ft all-arund, and make the crner seams watertight, this 6-ft by 6-ft by 1-ft bx, as shwn in figure 12-12, will flat. In fact, it will nt nly flat but will, in calm water, supprt an additinal 1,800 punds. 12-5
1' 1' 1' 1' It is bvius, then, that the vlume f the submerged part f a flating ship prvides the buyancy t keep the ship aflat. If the ship is at rest, the buyancy (which is the weight f the displaced water) must be equal t the weight f the ship. Fr this reasn, the weight f a ship is generally referred t as DISPLACEMENT, meaning the weight f the vlume f water displaced by the hull. Since weight (W) is equal t the displacement, it is pssible t measure the vlume f the underwater bdy (V) in cubic feet and multiply this vlume by the weight f a cubic ft f seawater t determine what the ship weighs. This relatinship may be written as the fllwing: (1) W = V 1 35 (2) V = 35W 6' DCf1212 Figure 12-12. A steel cube, and a bx made frm the same vlume f steel. V = Vlume f displaced seawater (in cubic feet) W = Weight in tns 35 = Cubic feet f seawater per tn (Fr ships, the lng tn f 2,240 punds is used.) 6' It is bvius that displacement will vary with the depth f a ship s keel belw the water line that is knwn as draft. As the draft increases, the displacement increases. This is indicated in figure 12-13 by a series f displacements shwn fr successive draft lines n the midship sectin f a ship. The vlume f an underwater bdy fr a given draft line can be measured in the drafting rm by using graphic r mathematical means. This is dne fr a series f drafts thrughut the prbable range f displacements in which a ship is likely t perate. The values btained are pltted n a grid n which feet f draft are measured vertically and tns f displacement hrizntally. A smth line is faired thrugh the pints pltted, prviding a curve f displacement versus draft, r a DISPLACEMENT CURVE as it is generally called. An example f this fr a typical warship is shwn in figure 12-14. T use the sample curve shwn in figure 12-14 fr finding the displacement when the draft is given, lcate the value f the mean draft n the draft scale at the left. Then prceed hrizntally acrss the diagram t the displacement curve. Frm this pint prceed vertically dwnward and read the displacement frm the scale. Fr example, if yu have a mean draft f 26 feet, the displacement fund frm the curve is apprximately 16,300 tns. Reserve uyancy The vlume f the watertight prtin f the ship abve the waterline is knwn as the ship s reserve buyancy. Expressed as a percentage, reserve buyancy is the rati f the vlume f the abve-water bdy t the vlume f the underwater bdy. Thus reserve buyancy may be stated as a vlume in cubic feet, as a rati r percentage, r as an equivalent weight f seawater in tns. (In tns it is 1/35 f the vlume in cubic feet f the abve-water bdy.) WATERLINE 28 FEET 24 FEET 20 FEET 16 FEET 12 FEET DISPLACEMENT 18,000 TONS 14,800 TONS 11,750 TONS 8,800 TONS 5,900 TONS Figure 12-13. Example f displacement data. DCf1213 12-6
32 30 28 DRAFT (FEET) 26 24 22 20 18 16 14 12 DISPLACEMENT IN SALT WATER AT 35 CUIC FEET PER TON 10 8 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 DISPLACEMENT (TONS - IN THOUSANDS) DCf1214 Figure 12-14. Example f a displacement curve. Freebard, a rugh measure f reserve buyancy, is the distance in feet frm the waterline t the weather deck edge. Freebard is calculated at the midship sectin. As indicated in figure 12-15, freebard plus draft always equals the depth f the hull in feet. WATERLINE RESERVE UOYANCY FREEOARD DRAFT DEPTH OF HULL The frce f gravity is a resultant r cmpsite frce, including the weights f all prtins f the ship s structure, equipment, carg, and persnnel. The frce f gravity may be cnsidered as a single frce, which acts dwnward thrugh the ship s center f gravity (G). The frce f buyancy is als a cmpsite frce, which results frm the pressure f the water n the ship s hull. A gd example f this is immersing a cntainer in a tank f water as shwn in view A f figure 12-16. The cntainer must be held under the water t keep it frm rising. View f figure 12-16 shws the psitin f the cntainer when it is released. DCf1215 Figure 12-15. Reserve buyancy, freebard, draft, and depth f hull. When weight is added t a ship, draft and displacement increase in the same amunt freebard and reserve buyancy decrease. It is essential t the seawrthiness f a ship t retain a substantial amunt f reserve buyancy. Sme ships can take mre than their wn weight in flding water abard withut sinking due t reserve buyancy. A Center f uyancy When a ship is flating at rest in calm water, it is acted upn by tw sets f frces: (1) the dwnward frce f gravity and (2) the upward frce f buyancy. Figure 12-16. A. An immersed cntainer;. The cntainer frced upward. 12-7
Hrizntal pressures n the sides f a ship cancel each ther under nrmal cnditins, as they are equal frces acting in ppsite directins (fig. 12-17). The vertical pressure may be regarded as a single frce the frce f buyancy acting vertically upward thrugh the CENTER OF UOYANCY (). G SCALE OF FEET - MEAN DRAFTS 34 32 30 28 26 24 22 20 18 16 14 CENTER OF UOYANCY AOVE ASE (K) 12 10 DCf1217 Figure 12-17. Relatinship f the frces f buyancy and gravity. When a ship is at rest in calm water, the frces f buyancy () and gravity (G) are equal and lie in the same vertical line, as shwn in figure 12-17. The center f buyancy, being the gemetric center f the ship s underwater bdy, lies n the centerline and usually near the midship sectin, and its vertical height is usually a little mre than half the draft. As the draft INCREASES, rises with respect t the keel. Figure 12-18 shws hw different drafts will create different values f the HEIGHT OF THE CENTER OF UOYANCY FROM THE KEEL (K). A series f values fr K (the center f buyancy frm the keel) is btained and these values are pltted n a curve t shw K versus draft. Figure 12-19 shws an example f a K curve fr a warship. 20 CL K 24 16 24 FOOT WATERLINE 20 FOOT WATERLINE 16 FOOT WATERLINE ASE LINE DCf1218 Figure 12-18. Successive centers f buyancy () fr different drafts. 8 8 9 10 11 12 13 14 15 16 T read K when the draft is knwn, start at the prper value f the draft n the scale at the left (fig. 12-19) and prceed hrizntally t the curve. Then drp vertically dwnward t the baseline (K). Thus, if ur ship were flating at a mean draft f 19 feet, the K fund frm the chart wuld be apprximately 11 feet. Inclining Mments K - FEET DCf1219 Figure 12-19. Curve f center f buyancy abve base. A ship may be disturbed frm rest by cnditins which tend t make it heel ver t an angle. These cnditins include such things as wave actin, wind pressures, turning frces when the rudder is put ver, recil f gunfire, impact f a cllisin r enemy hit, shifting f weights n bard, and additin f ff-center weights. These cnditins exert heeling mments n the ship that may be temprary r cntinuus. When a disturbing frce exerts an inclining mment n a ship, there is a change in the shape f the ship s underwater bdy. The underwater vlume is relcated, its bulk being shifted in the directin f the heel. This cnditin causes the center f buyancy () t leave the ship s centerline and shift in the directin f the heel. (The center f buyancy mves t the gemetric center f the new underwater bdy.) As a result, the lines f actin f the frces f buyancy and gravity separate and in ding s exert a MOMENT n the ship. This mment tends t restre the ship t an even keel. 12-8
If yu study figure 12-20, yu will ntice that a RIGHTING r RESTORING MOMENT is present. This righting mment is caused by the tw equal and ppsite frces, each f W tns (displacement) magnitude, separated by a distance GZ, which cnstitutes the LEVER ARM OF MOMENT. Figure 12-20 shws that the ship is stable because the center f buyancy () has shifted far enugh t psitin the buyant frce where it tends t restre the ship t an even keel r an upright psitin. Hwever, it is pssible fr cnditins t exist which d nt permit t mve far enugh in the directin in which the ship rlls t place the buyant frce utbard f the frce f gravity. The mment prduced will tend t upset the ship, rendering it unstable. Figure 12-21 shws an unstable ship in which the relative psitins f and G prduce an UPSETTING MOMENT. In this illustratin it is bvius that the cause f the upsetting mment is the high psitin f G (center f gravity) and the GEOMETRIC CENTER OF THE UNDERWATER ODY ( the center f buyancy). ANGLE OF HEEL G Z DIRECTION OF RIGHTING MOMENT FORCE OF UOYANCY ANGLE OF HEEL Z G DIRECTION OF UPSETTING MOMENT FORCE OF GRAVITY DCf1220 Figure 12-20. Develpment f righting mment when a stable ship inclines. A mment is the prduct f a frce tending t prduce a rtatin abut an axis times its distance frm the axis. If tw equal and ppsite frces are separated by a distance, the mment will becme a cuple which is measured by ONE f the frces times the distance that separates them. The RIGHTING MOMENT f a ship is therefre the prduct f the frce f buyancy times the distance GZ (fig. 12-20) that separates the frces f buyancy and gravity. It may als be expressed as the frce f gravity (weight f the ship) times GZ. The distance GZ is knwn as a ship s RIGHTING ARM. Putting this int mathematical terms, yu have the fllwing: Righting mment = W x GZ (expressed in ft-tns) Where: W = displacement in tns GZ = righting arm in feet Fr example, if a ship displaces 10,000 tns and has a 2-ft righting arm at 40 inclinatin, the righting mment is 10,000 tns times 2 feet, r 20,000 ft-tns. These 20,000 ft-tns represent the frce, which tends t return the ship t an upright psitin. Metacenter FORCE OF GRAVITY DCf1221 Figure 12-21. Develpment f an upsetting mment when an unstable ship inclines. A ship s METACENTER (M) is the intersectin f tw successive lines f actin f the frce f buyancy, as the ship heels thrugh a very small angle. Figure 12-22 shws tw lines f buyant frce. One f these represents the ship n even keel, the ther at a small angle f heel. The pint where they intersect is the initial psitin f the metacenter. When the angle f heel is greater than the angle used t cmpute the metacenter, M mves ff the centerline and the path f mvement is a curve. ANGLE OF HEEL IS EXAGGERATED UOYANT FORCE UPRIGHT 1 C L M 2 UOYANT FORCE INCLINED Figure 12-22. The metacenter. WATERLINE UPRIGHT WATERLINE INCLINED TO A VERY SMALL ANGLE DCf1222 12-9
The INITIAL psitin f the metacenter is mst useful in the study f stability, because it prvides a reference pint when the ship is upright and mst stable. In ur discussin we will refer t initial psitin f M. The distance frm the center f buyancy () t the metacenter (M) when the ship is n even keel is the METACENTRIC RADIUS. Metacentric Height The distance frm the center f gravity (G) t the metacenter is knwn as the ship s METACENTRIC HEIGHT (GM). Figure 12-23, view A, shws a ship heeled thrugh a small angle (the angle is exaggerated in the drawing), establishing a metacenter at M. The ship s righting arm is GZ, which is ne side f the triangle GZM. In this triangle GZM, the angle f heel is at M. The side GM is perpendicular t the waterline at even keel, and ZM is perpendicular t the waterline when the ship is inclined. ANGLE OF HEEL G M Z ANGLE OF HEEL G M Z The ship s METACENTRIC HEIGHT (GM) is nt nly a measure f the ship s RIGHTING ARM (GZ) but is als an indicatin f whether the ship is stable r unstable. If M is abve G, the metacentric height is psitive, the mments which develp when the ship is inclined are RIGHTING MOMENTS, and the ship is stable, as shwn in view A f figure 12-23. ut if M is belw G, the metacentric height is negative, the mments that develp are UPSETTING MOMENTS, and the ship is unstable, as shwn in view f figure 12-23. Influence f Metacentric Height If the metacentric height (GM) f a ship is large, the righting arms that develp, at small angles f heel, will be large. Such a ship is stiff and will resist rll. Hwever, if the metacentric height f a ship is small, the righting arms that develp will be small. Such a ship is tender and will rll slwly. In ships, large GM and large righting arms are desirable fr resistance t damage. Hwever, a smaller GM is smetimes desirable fr a slw, easy rll that allws fr mre accurate gunfire; therefre, the GM value fr a naval ship is the result f cmprmise. C L Inclining Experiment Z A G C L The ship designer uses calculatins t determine the vertical psitin f the center f gravity. Frm available plans and data, the varius items that g t make up the ship and its lad are tabulated. The ship can be cnsidered as cnsisting f the varius parts f the structure, machinery, and equipment. The lad is cmprised f fuel, il, water, ammunitin, and sundry stres abard. M DCf1223 Figure 12-23. A. Stable cnditin, G is belw M;. Unstable cnditin, G is abve M. It is evident that fr any given angle f heel, there will be a definite relatinship between GM and GZ because GZ = GM sin θ. Thus GM acts as a measure f GZ, the righting arm. Althugh the psitin f the center f gravity as estimated by calculatin is sufficient fr design purpses, an accurate determinatin is required t establish the verall stability f the ship when it is perating. Therefre, an inclining experiment is perfrmed t btain accurately the vertical height f the center f gravity abve the keel (KG) when the ship is cmpleted. An inclining experiment cnsists f mving ne r mre large weights acrss the ship and measuring the angle f list prduced. This angle f list usually des nt exceed 2. The ship shuld be in the best pssible cnditin fr the inclining. The naval shipyard r building yard at which the inclining experiment is t be perfrmed issues a memrandum t 12-10
the cmmanding fficer f the ship utlining the necessary wrk t be dne by the ship s frce and by the yard t prepare the ship fr the inclining. The results f the experiment are furnished t each ship as a bklet f inclining experiment data. This bklet cntains data n displacement, the center f gravity abve the keel (KG), and verall stability fr the perating cnditins f lad. Detailed infrmatin n the inclining experiment can be btained frm Naval Ships Technical Manual (NSTM), chapter 096, Weights and Stability. Q1. Detailed infrmatin n the laws f mathematics and physics used t determine the buyancy and stability f a ship are prvided in Naval Ships Technical Manual (NSTM), chapter 079, vlume 1, and in NSTM, chapter 096. 1. True 2. False Q2. Which f the fllwing trignmetric functins is NOT used fr making calculatins t determine a ship s stability? 1. Csine 2. Sine 3. Tangent 4. Ctangent Q3. Which f the fllwing terms best defines frce multiplied by the distance frm an axis abut which yu want t find its effect? 1. Mment f frce 2. Frictin 3. allast 4. Inclining mment Q4. The vlume f water that is mved by the hull f a ship is knwn as displacement. 1. True 2. False REVIEW QUESTIONS Q5. What measurement is knwn by the term freebard? 1. Distance in feet frm the keel t the waterline 2. Distance frm the waterline t the weather deck edge 3. Distance frm the bw t the stern 4. Distance frm the prtside t the starbard side f the ship Q6. Which f the fllwing infrmatin is NOT cntained in the bklet f inclining experiment data? 1. Data n displacement 2. The center f gravity abve the keel 3. Reserve buyancy 4. Overall stability ANALYSIS OF STAILITY Learning Objectives: Recall the laws f physics and trignmetry used t determine stability and buyancy f a ship; and the effects f buyancy, gravity, and weight shifts n ship stability. T analyze stability principles, yu must be familiar with the terms, definitins, and equatins that are used t express imprtant relatinships. These are listed belw. G, the ship s center f gravity, is the pint at which all weights f the ship may be cnsidered t be cncentrated. The frce f gravity is cnsidered as acting straight dwnward, thrugh the center f gravity, at right angles t the waterline., the ship s center f buyancy, is at the gemetric center f the ship s underwater hull. When a ship is at rest in calm water, the frces f and G are equal and ppsite, and the pints and G lie in the same vertical line. When the ship is inclined, and G mve apart, since mves ff the ship s centerline as a result f the change in the shape f the underwater hull. M, the ship s metacenter, is a pint established by the intersectin f tw successive lines f buyant frce as the ship heels thrugh a very small angle. 12-11
GM, metacentric height, is the distance frm G t M; it is measured in feet. Z is the pint at which a line, thrugh G, parallel t the waterline, intersects the vertical line thrugh. GZ, the distance frm G t Z, is the ship s righting arm; it is measured in feet. Fr small angles f heel, GZ may be expressed by the equatin GZ = GM sin θ W is the weight (displacement) f the ship; it is measured in lng tns. K is a pint at the bttm f the keel, at the midship sectin, frm which all vertical measurements are made. K is the vertical distance frm K t the center f buyancy when the ship is upright. K is measured in feet. KG is the vertical distance frm K t the ship s center f gravity when the ship is upright. KG is measured in feet. KM is the vertical distance frm K t the metacenter when the ship is upright. KM is measured in feet. The RIGHTING MOMENT f a ship is W times GZ, that is, the displacement times the righting arm. Righting mments are measured in ft-tns. Since the righting arm (GZ) is equal t GM times sin θ, fr small values f θ, yu can say that the righting mment is equal t W times GM times sin θ. ecause f the relatinship between righting arms and righting mments, it is bvius that stability may be expressed either in terms f GZ r in righting mments. Hwever, yu must be very careful nt t cnfuse righting arms with righting mments; they are NOT identical. STAILITY CURVES When a series f values fr GZ (the ship s righting arm) at successive angles f heel are pltted n a graph, the result is a STAILITY CURVE. The stability curve, as shwn in figure 12-24, is called the CURVE OF STATIC STAILITY. The wrd static indicates that it is nt necessary fr the ship t be in mtin fr the curve t apply. If the ship is mmentarily stpped at any angle during its rll, the value f GZ given by the curve will still apply. NOTE The stability curve is calculated graphically by design engineers fr values indicated by angles f heel abve 7. 3 GZ(RIGHTING ARM) IN FEET 2 1 0 10 20 30 40 50 60 70 80 90 ANGLE OF HEEL, IN DEGREES G G Z G Z G Z G WATERLINE ANGLE OF HEEL = 0 ANGLE OF HEEL = 20 ANGLE OF HEEL = 40 ANGLE OF HEEL = 60 ANGLE OF HEEL = 70 GZ=0 GZ = 1.33 FEET GZ = 2.13 FEET GZ = 1 FOOT GZ=0 Figure 12-24. Curve f static stability. DCf1224 12-12
T understand this stability curve, it is necessary t cnsider the fllwing facts: 1. The ship s center f gravity des NOT change psitin as the angle f heel is changed. 2. The ship s center f buyancy is always at the gemetric center f the ship s underwater hull. 3. The shape f the ship s underwater hull changes as the angle f heel changes. If these three facts are cnsidered cllectively, yu will see that the psitin f G remains cnstant as the ship heels thrugh varius angles, but the psitin f changes accrding t the angle f inclinatin. When the psitin f has changed s that and G are nt in the same vertical line, a righting arm GZ must exist. The length f this righting arm depends upn the angle at which the ship is inclined (fig. 12-25). GZ increases as the angle f heel increases, up t a certain pint. At abut an angle f 40, the rate f increase f GZ begins t level ff. The value f GZ diminishes and finally reaches zer at a very large angle f heel. A reductin in the size f the righting arm usually means a decrease in stability. When the reductin in GZ is caused by increased displacement, hwever, the ttal effect n stability is mre difficult t evaluate. Since the RIGHTING MOMENT is equal t W times GZ, it will be increased by the gain in W at the same time that it is decreased by the reductin in GZ. The gain in the righting mment, caused by the gain in W, des nt necessarily cmpensate fr the reductin in GZ. In summary, there are several ways in which an increase in displacement affects the stability f a ship. Althugh these effects ccur at the same time, it is best t cnsider them separately. The effects f increased displacement are the fllwing: 1. RIGHTING ARMS (GZ) are decreased as a result f increased draft. 2. RIGHTING MOMENTS (ft-tns) are decreased as a result f decreased GZ. 3. RIGHTING MOMENTS are increased as a result f the increased displacement (W). Crss Curves f Stability 20 20 FORCE OF UOYANCY AT 26 FOOT DRAFT AND 20 HEEL Z 26 G 26 Z18 18 Effect f Draft n Righting Arm FORCE OF UOYANCY AT 18 FOOT DRAFT AND 20 HEEL 26 FOOT WATERLINE AT 20 ANGLE OF HEEL 18 FOOT WATERLINE AT 20 ANGLE OF HEEL 26 FOOT WATERLINE AT EVEN KEEL 18 FOOT WATERLINE AT EVEN KEEL Figure 12-25. Effect f draft n righting arm. DCf1225 A change in displacement will result in a change f draft and freebard; and will shift t the gemetric center f the new underwater bdy. At any angle f inclinatin, a change in draft causes t shift bth hrizntally and vertically with respect t the keel. The hrizntal shift in changes the distance between and G, and thereby changes the length f the righting arm, GZ. Thus, when draft is increased, the righting arms are reduced thrughut the entire range f stability. Figure 12-25 shws hw the righting arm is reduced when the draft is increased frm 18 feet t 26 feet when the ship is inclined at an angle f 20. The psitin f the center f buyancy at any given angle f inclinatin depends upn the draft. As the draft increases, the center f buyancy mves clser t the center f gravity, thereby reducing the length f the righting arms. T determine this effect, the design activity inclines a line drawing f the ship s lines at a given angle, and then lays ff a series f waterlines n it. These waterlines are chsen at evenly spaced drafts thrughut the prbable range f displacements. Fr each waterline the value f the righting arm is calculated, using an ASSUMED center f gravity, rather than the TRUE center f gravity. A series f such calculatins is made fr varius angles f heel usually 10, 20, 30, 40, 50, 60, 70, 80, and 90 and the results are pltted n a grid t frm a series f curves knwn as the CROSS CURVES OF STAILITY. Figure 12-26 is an example f a set f crss curves. Nte that, as draft and displacement increase, the curves all slpe dwnward, indicating increasingly smaller righting arms. The crss curves are used in the preparatin f stability curves. T take a stability curve frm the crss curves, draw a vertical line (such as line MN in fig. 12-26) n the crss curve sheet at the displacement that crrespnds t the mean draft f the ship. At the intersectin f this vertical line with each crss curve, 12-13
N... 263-16 INCLINING EXPERIMENT, U. S. S. NEVERSAIL (Sheet f ) Axis assumed feet abve base line Vessel cnsidered water-tight t Taken frm Plan N. Scale f Tns Displacement 9,000 10,000 11,000 M 12,000 13,000 6 uships N. 14,000 15,000 NATURAL SINE ANGLE SINE ANGLE SINE 0 0 50.7660 10.1736 60.8660 20.3420 70.9397 30.5000 80.9948 40.6428 90 1.0000 Scale f Righting Arms - Feet 5 4 3 2 50 40 60 70 30 80 20 90 (e) (d) (f) (g) (c) (h) (b) (i) 50 40 60 70 30 80 20 90 10 1 (a) 10 0 N DCf1226 Figure 12-26. Example f crss curves f stability. read the crrespnding value f the righting arm n the vertical scale at the left. Then plt this value f the righting arm at the crrespnding angle f heel n the grid fr the stability curve. When yu have pltted a series f such values f the righting arms frm 10 t 90 f heel, draw a smth line thrugh them and yu have the UNCORRECTED stability curve fr the ship at that particular displacement. In figure 12-27, curve A represents an uncrrected stability curve fr the ship while perating at 11,500 tns displacement, taken frm the crss curves shwn in figure 12-26. This stability curve cannt be used in its present frm, since the crss curves are made up n the basis f an assumed center f gravity. In actual peratin, the ship s cnditin f lading will affect its displacement and therefre the lcatin f the ship s center f gravity (G). T use a curve taken frm the crss curves, therefre, it is necessary t crrect the curve fr the ACTUAL height f G abve the keel (KG). If the distance KG is nt knwn and a number f weights have been added t r remved frm a ship, KG can be fund by the use f vertical mments. A vertical mment is the prduct f the weight times its vertical height abve the keel. As far as the new center f gravity is cncerned, when a weight is added t a system f weights, the center f gravity can be fund by taking mments f the ld system plus that f the new weight and dividing this ttal mment by the ttal final weight. Detailed infrmatin cncerning changes in the center f gravity f a ship can be btained frm Naval Ships Technical Manual (NSTM), chapter 096. 12-14
RIGHTING ARM IN FEET 6 5 4 3 2 1 (a) (b) (c) (d) 0 10 20 30 40 50 60 70 80 90 ANGLE OF HEEL IN DEGREES Suppse that the crss curves are made up n the basis f an assumed KG f 20 feet and that yu determine that the actual KG is 24 feet fr the particular cnditin f lading. This means that the true G is 4 feet higher than the assumed G and that the righting arm (GZ) at each angle f inclinatin will be SMALLER than the righting arm shwn in figure 12-27 (curve A) fr the same angle. T find the new value f GZ fr each angle f inclinatin, multiply the increase in KG (4 feet) by the sine f the angle f inclinatin, and SUTRACT this prduct frm the value f GZ shwn n the crss curves r n the uncrrected stability curve. In rder t facilitate the crrectin f the stability curves, a table shwing the necessary sines f the angles f inclinatin is included n the crss curves frm. Next, find the crrected values f GZ fr the varius angles f heel shwn n the stability curve (A) in figure 12-27, and plt them n the same grid t make the crrected stability curve () shwn in figure 12-27. At 10, the uncrrected value f GZ is 1.4; therefre, the crrected GZ at 10 is 1.4 minus (4 x 0.1736), r 0.7056. At 20, the uncrrected value f GZ is 2.8; therefre, the crrected GZ at 20 is 2.8 minus (4 x 0.3420), r 1.4320. Repeating this prcess at 30, 40, 50, 60, 70, and 80, the fllwing values are btained: (e) At 30, the crrected GZ = 2.2000 At 40, the crrected GZ = 2.3288 At 50, the crrected GZ = 2.2360 At 60, the crrected GZ = 1.4360 (f) (g) (h) A (i) DCf1227 Figure 12-27. A. Uncrrected stability curve taken frm crss curves;. Crrected stability curve. At 70, the crrected GZ = 0.5412 At 80, the crrected GZ = minus 0.4392 It is nt necessary t figure the crrected GZ at 90, since the value is already negative at 80. When the values frm 10 thrugh 80 are pltted n the grid and jined with a smth curve, the CORRECTED stability curve () shwn in figure 12-27 results. As yu can see, the crrected curve shws maximum stability t be at 40 ; it als shws that an upsetting arm, rather than a righting arm, generally exists at angles f heel in excess f 75. EFFECTS OF LOOSE WATER When a tank r a cmpartment in a ship is partially full f liquid that is free t mve as the ship heels, the surface f the liquid tends t remain level. The surface f the free liquid is referred t as FREE SURFACE. The tendency f the liquid t remain level as the ship heels is referred t as FREE SURFACE EFFECT. The term LOOSE WATER is used t describe liquid that has a free surface; it is NOT used t describe water r ther liquid that cmpletely fills a tank r cmpartment and thus has n free surface. Free Surface Effect Free surface in a ship causes a reductin in GM, due t a change in the center f gravity, and a cnsequent reductin in stability. The free surface effect is separate frm and independent f any effect that may result merely frm the additin f the weight f the liquid. When free surface exists, a free surface crrectin must be included in stability calculatins. Hwever, when a tank is cmpletely filled s that there is n free surface, the liquid in the tank may be treated as a slid; that is, the nly effect f the liquid n stability is the effect f its weight at its particular lcatin. T understand the actins that ccur because f free surface effect, use a centerline cmpartment that is partially full f water, as shwn in figure 12-28, as an example. L4 L3 L2 W1 L1 W L W 2 l 4 W 3 w l W4 F w 4 E D Figure 12-28. Effects f free surface. DCf1228 12-15
T begin with, the ship is flating n an even keel at waterline WL. Then the cmpartment is flded t waterline W 1. Assuming that the water enters the cmpartment instantaneusly and that it is instantaneusly frzen slid, the effects f this frzen bdy f water are the same as if a slid weight had been added. The ship underges parallel sinkage and cmes t rest at a new waterline W 1 L 1. Nw suppse that an utside frce acts n the ship, causing it t heel ver at a small angle f list t a new waterline W 2 L 2. If at the same time the liquid is freed frm its frzen state, it will run tward the lw side f the cmpartment until the surface f the water in the cmpartment is parallel t the existing waterline W 2 L 2. A wedge f liquid is thus shifted frm ne side f the cmpartment t the ther; as a result, the center f gravity f the liquid is shifted frm D t E. As the center f gravity f the liquid is shifted utbard, an additinal inclining mment is created. This causes the ship t list t a new waterline W 3 L 3. The additinal list, in turn, causes a further shift f the liquid in the cmpartment and a further shift f the center f gravity f the liquid. As the center f gravity f the liquid shifts t F, anther inclining mment is created and the ship lists even mre. Eventually the ship will cme t rest with a waterline such as W 4 L 4. This will ccur when the righting mment f the ship is equal t the cmbined effects f (1) the riginal inclining mment created by the utside frce and (2) the inclining mment created by the shift f liquid within the cmpartment. Lcatin f Free Surface The free surface effect is independent f the lcatin f the free surface within the ship. A free surface with a certain length and breadth will, at any given angle f heel, cause the same reductin in GM (and, therefre, the same lss f stability) n matter where it is in the ship frward r aft, high r lw, n the centerline r ff the centerline. Depth f Lse Water The free surface effect f a given area f lse water at a given angle f heel des NOT depend upn the depth f the lse water in the tank r cmpartment, unless the lse water is shallw enugh r deep enugh t cause the effect knwn as pcketing f the free surface. Pcketing ccurs when the free surface f the liquid cmes in cntact with the deck r the verhead and causes a reductin in the breadth f the free surface. T understand hw pcketing f the free surface reduces the free surface effect, study figure 12-29. View A f figure 12-29 shws a cmpartment in which the free surface effect is NOT influenced by the depth f the lse water. The cmpartment shwn in view, hwever, cntains nly a small amunt f water. When the ship heels sufficiently t reduce the waterline in the cmpartment frm w1 t W 1 l 1, the breadth f the free surface is reduced and the free surface effect is thereby reduced. A similar reductin in free surface effect ccurs in the almst full cmpartment shwn in view C, again because f the reductin in the breadth f the free surface. As figure 12-29 shws, the beneficial effect f pcketing is greater at larger angles f heel. w w 1 A PARTIALLY FULL w w 1 w w 1 l 1 l SHALLOW C ALMOST FULL DCf1229 The reductin in free surface effect that results frm pcketing is NOT taken int cnsideratin when evaluating stability. Since pcketing imprves stability, neglecting this factr in stability calculatins prvides a margin f safety; hwever, in centerline deep tanks n l 1 l 1 l Figure 12-29. Diagram t illustrate pcketing f free surface. l 12-16
sme ships in which the tank is higher than wide, the ppsite may be true. The nrmal practice f maintaining the fuel il tanks 95 percent full takes advantage f the fact that pcketing ccurs, at very small angles f heel, when a cmpartment is almst full. Length and readth f Free Surface The athwartship breadth f a cmpartment has a great influence n the reductin in GM caused by the free surface effect. This influence is shwn by the fllwing frmula: Rise in G b1 3 12(35W) Where b = athwartship breadth f cmpartment 1 = fre-and-aft length f cmpartment W = displacement f ship As indicated by this frmula, the free surface effect varies as the cube f the breadth (b) but nly as the first pwer f the length (l). ecause f this relatinship, a single bulkhead that cuts a cmpartment in half in a fre-and-aft directin will quarter the free surface effect. Chart fr Calculating Free Surface Effect T avid having t make calculatins frm the frmula given in the previus sectin, a free surface effect chart based n this frmula is used t find the reductin in GM that ccurs as a result f free surface. Such a chart is shwn in figure 12-30. T use this chart, draw a straight line frm the apprpriate pint n the ATHWARTSHIP DIMENSION scale (A) t the apprpriate pint n the C A CHART FOR 100 FREE SURFACE EFFECT 100 ASED ON EQUATION 90 b RISE IN G = 3 90 l 12 (35w) 80 80 b = READTH OF COMPARTMENT I = LENGTH OF COMPARTMENT 70 w = DISPLACEMENT OF SHIP 70 D 500 600 700 800 900 1,000 60 60 E 1,500 50 40 30 ATHWARTSHIP DIMENSION IN FEET PIVOT 10.0 5.0 4.0 3.0 2.0 GM REDUCTION IN FEET 25.1 25 20 1.0.7.5.4.3.2.05.04.03.02 1 2 50 40 30 20 LONGITUDINAL DIMENSION IN FEET DISPLACEMENT IN TONS 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 15,000 10.01 10 20,000 30,000 40,000 0 10 50,000 Figure 12-30. Chart fr calculating free surface effect. DCf1232 12-17
LONGITUDINAL DIMENSION scale (); this line will intersect the pivt scale. Then draw a secnd straight line frm the pint f intersectin n the pivt scale (C) t the apprpriate pint n the displacement scale (D). The pint at which this secnd straight line intersects the GM reductin scale (E) gives yu the reductin in GM (in feet) that is caused by the free surface. Fr example, assume that yu want t find what reductin in GM is caused by free surface effect in a partially flded cmpartment that is 35 feet athwart ships and 20 feet fre-and-aft, in a ship f 10,000 tns displacement. Draw the first straight line frm the 35-ft pint n the athwartship dimensin scale t the 20-ft pint n the lngitudinal dimensin scale. Then draw the secnd straight line frm the pint f intersectin n the pivt line t the 10,000-tn pint n the displacement scale. The pint at which the secnd straight line intersects the GM reductin scale indicates hw much reductin in GM has ccurred because f free surface effect in the partially flded cmpartment. In this example, GM has been reduced 0.2 ft. Free Cmmunicatin Effect Thus far, the stability changes caused by the effect f free surface and by the additin f the weight f the flding water have been cnsidered. In certain instances, it is als necessary t make allwance fr stability changes that ccur when an ff-center cmpartment is in free cmmunicatin with the sea. If a bundary f an ff-center cmpartment is s extensively ruptured that the sea can flw freely in and ut as the ship rlls, the FREE COMMUNICATION EFFECT will cause a reductin in GM and in GZ. Nte that the free cmmunicatin effect n stability is IN ADDITION TO the effect f free surface and the effect f added weight. T understand the free cmmunicatin effect, cnsider an ff-center cmpartment partially full f water and in free cmmunicatin with the sea, as shwn in figure 12-31. (Nte that this cmpartment is free t vent at the tp.) efre the hull is ruptured, the ship flats n an even keel at waterline WL. Then the cmpartment is partially flded and left in free cmmunicatin with the sea. Assume that the water enters the cmpartment instantaneusly (up t the level f the ship s riginal waterline WL) and is instantaneusly frzen slid. If the weight f the frzen water is distributed equally abut the ship s centerline, the ship will underg parallel sinkage t a new waterline such as W 1 l 1. Since the weight is ff center, hwever, the ship assumes an inclined psitin with a waterline similar t W 2 L 2. W1 W W2 W3 W4 If the water in the cmpartment is nw returned t its fluid state, it will have a waterline a-b that is parallel t (but belw) the ship s waterline W 2 L 2. Immediately, hwever, additinal water will flw in frm the sea and fld the cmpartment t the actual level f the ship s waterline W 2 L 2. The ship will therefre sink deeper in the water and will assume a greater list; the waterline will reach a psitin such as W 3 L 3. Again, additinal water will flw in frm the sea and fld the cmpartment t the level f the ship s waterline W 3 L 3 ; this will cause the ship t sink even deeper in the water and t assume an even greater list. These interactins will cntinue until the waterline is at the psitin represented by W 4 L 4. Nte that stability is nt usually reduced by free cmmunicatin if the cmpartment is symmetrical abut the ship s centerline. Under certain circumstances, free cmmunicatin in a centerline cmpartment may increase the free surface effect, and thereby reduce stability. Hwever, it is imprtant t remember that this reductin in stability ccurs frm the increased free surface effect, rather than frm any free cmmunicatin effect. Summary f Effects f Lse Water C L L4 L3 L2 DCf1231 Figure 12-31. Free cmmunicatin effect in ff-center cmpartment. The additin f lse water t a ship alters the stability characteristics by means f three effects that must be cnsidered separately: (1) the effect f added a b L1 L 12-18
weight, (2) the effect f free surface, and (3) the effect f free cmmunicatin. Figure 12-32 shws the develpment f a stability curve with crrectins fr added weight, free surface, and free cmmunicatin. Curve A is the ship s riginal stability curve befre flding. Curve represents the situatin after flding; this curve shws the effect f added weight (increased stability) but it des NOT shw the effects f free surface r f free cmmunicatin. Curve C is curve crrected fr free surface effect nly. Curve D is curve crrected fr bth free surface effect and free cmmunicatin effect. Curve D, therefre, is the final stability curve; it incrprates crrectins fr all three effects f lse water. RIGHTING ARM IN FEET 4 3 2 1 0 10 20 30 40 50 60 70 80 90 ANGLE OF HEEL IN DEGREES DCf1232 LONGITUDINAL STAILITY CURVE CURVE A CURVE C CURVE D Figure 12-32. Develpment f stability curve crrected fr effects f added weight, free surface, and free cmmunicatin. Thus far in studying stability, yu have been cncerned nly with TRANSVERSE STAILITY and with TRANSVERSE INCLINATIONS. LONGI- TUDINAL STAILITY and LONGITUDINAL INCLINATIONS, r TRIM, shuld als be cnsidered. Trim is measured by the difference between the frward draft and the after draft. When the after draft is greater than the frward draft, the ship is said t be TRIMMED Y THE STERN. When the frward draft is greater than the after draft, the ship is said t be TRIMMED Y THE OW r TRIMMED Y THE HEAD. As a ship trims, it inclines abut an athwartship axis that passes thrugh a pint knwn as the CENTER OF FLOTATION (CF). The mean draft that is used t enter the draft scale t read a displacement curve is the draft amidships. When a ship has trim, hwever, neither the draft amidships nr the average f the frward and after drafts will give a true mean draft. Fr mst types f ships, the curves f frm may be used withut crrectin fr trim, PROVIDED the trim is less than abut 1 percent f the length f the ship. When the trim is greater, hwever, the readings btained frm the curves f frm must be crrected fr trim. Lngitudinal stability is the tendency f a ship t resist a change in trim. The lngitudinal metacentric height multiplied by the displacement is taken as a measure f INITIAL lngitudinal stability when trim is very small. (It is imprtant t nte that the lngitudinal metacenter (M1) is NOT the same as the transverse metacenter.) A mre accurate measure f the ship s ability t resist a change f trim is made in terms f the mment required t prduce a change in trim f a definite amunt. The MOMENT TO CHANGE TRIM 1 INCH (MTI) is used as the standard measure f resistance t lngitudinal inclinatin. REVIEW QUESTIONS Q7. The ship s center f gravity is the pint at which all weights f the ship may be cnsidered t be cncentrated. The frce f gravity is cnsidered as acting straight dwnward, thrugh the center f gravity, at right angles t the waterline. 1. True 2. False Q8. Detailed infrmatin cncerning changes in the center f gravity f a ship can be btained frm which f the fllwing NSTMs? 1. NSTM, chapter 096 2. NSTM, chapter 040 3. NSTM, chapter 033 4. NSTM, chapter 010 Q9. Which f the fllwing terms is used t describe water r ther liquid that has a free surface? 1. Reserve buyancy 2. Reserve ballast 3. Draft 4. Lse water 12-19
Q10. What effect des pcketing have n stability? 1. Imprves stability 2. Imprves righting arms 3. Imprves buyancy 4. Imprves righting mments Q11. Which f the fllwing effects des NOT alter the stability characteristics f a ship when yu have lse water? 1. Added weight 2. Free surface 3. Free cmmunicatin 4. Added buyancy Q12. What des lngitudinal stability resist? 1. Change in trim 2. Change in list 3. Draft 4. Heeling SUMMARY This chapter has intrduced yu t the terminlgy used fr ship stability; the laws f physics and trignmetry used t determine stability and buyancy f a ship; and the effects f buyancy, gravity, and weight shifts n ship stability. Other aspects invlved in the study f stability are taken int cnsideratin when an inclining experiment is being cnducted, when the ship is being dry dcked, r when a grunding has ccurred. Abard certain ships yu may qualify as ballasting fficer and be actively invlved in maintaining stability. Remember that additinal infrmatin n this tpic may be fund in the fllwing publicatins: Naval Ships Technical Manual (NSTM), chapter 079, vlume 1, and chapter 096; nnresident training curses (NRTCs): Mathematics, vlume 1; Mathematics, vlume 2A; Fireman; and asic Machines. 12-20
REVIEW ANSWERS A1. Detailed infrmatin n the laws f mathematics and physics used t determine the buyancy and stability f a ship are prvided in Naval Ships Technical Manual (NSTM), chapter 079, vlume 1, and in NSTM, chapter 096. (1) True A2. Which f the fllwing trignmetric functins is NOT used fr making calculatins t determine a ship s stability? (4) Ctangent A3. Which f the fllwing terms best defines frce multiplied by the distance frm an axis abut which yu want t find its effect? (1) Mment f frce A4. The vlume f water that is mved by the hull f a ship is knwn as displacement. (1) True A5. What measurement is knwn by the term freebard? (2) Distance frm the waterline t the weather deck edge A6. Which f the fllwing infrmatin is NOT cntained in the bklet f inclining experiment data? (3) Reserve buyancy A7. The ship s center f gravity, is the pint at which all weights f the ship may be cnsidered t be cncentrated. The frce f gravity is cnsidered as acting straight dwnward, thrugh the center f gravity, at right angles t the waterline. (1) True A8. Detailed infrmatincncerning changes in the center f gravity f a ship can be btained frm which f the fllwing NSTMs? (1) NSTM, chapter 096 A9. Which f the fllwing terms is used t describe water r ther liquid that has a free surface? (4) Lse water A10. What effect des pcketing have n stability? (1) Imprves stability A11. Which f the fllwing effects des NOT alter the stability characteristics f a ship when yu have lse water? (4) Added uyancy A12. What des lngitudinal stability resist? (1) Change in trim 12-21