Principles of naval engineering - Historic Naval Ships Association

^Chapter S-STABILITY AND BUOYANCYANGLE OFHEELdamage. However, a smaller GM is sometimesdesirable for the slow, easy roll which makes formore accurate gunfire. Thus the GM value fora naval ship is the result of compromise.STABILITY CURVESWhen a series of values for GZ at successiveangles of heel are plotted on a graph, the resultis a stability curve . The stability curve shown infigure 3-12 is called a curve of static stability .The word static indicates that it is not necessaryfor the ship to be in motion for the curve toapply; if the ship were momentarily stopped atany angle during its roll, the value of GZ givenby the curve would still apply.To understand the stability curve, it is necessaryto consider the following facts:1. The ship's center of gravity does notchange position as the angle of heel is changed.2. The ship's center of buoyancy is alwaysat the center of the ship's underwater hull.3. The shape of the ship's underwater hullchanges as the angle of heel changes.Putting these facts together, we see that theposition of G remains constant as the ship heelsthrough various angles, but the position of Bchanges according to the angle of inclination.Initial stability increases with increasing angleof heel at an almost constant rate; but at largeangles the increase in GZ begins to level off andgradually diminishes, becoming zero at verylarge angles of heel.EFFECT OF DRAFT ON RIGHTING ARM8.55Figure 3-11. — (A) Stable condition, G is belowM. (B) Unstable condition, G is above M.metacentric height is small, the righting armsare also small. Such a ship rolls slowly and issaid to be tender . Some GM values for variousnaval ships are: CLs, 3 to 5 feet; CAs, 4 to 6feet; DDs, 3 to 4 feet; DEs, 3 to 5 feet; and AKs,1 to 6 feet.Large GM and large righting arms are desirablefor resistance to the flooding effects ofA change in displacement will result in achange of draft and freeboard; and B will shiftto the geometric center of the new underwaterbody. At any angle of inclination, a change indraft causes B to shift both horizontally andvertically with respect to the waterline. Thehorizontal shift in B changes the distance betweenB and G, and thereby changes the lengthof the righting arm. GZ. Thus, when draft isincreased, the righting arms are reducedthroughout the entire range of stability. Figure3-13 shows how the righting arm is reducedDesign engineers usually use GM values as a measureof stability up to about 7 heel. For angles beyond 7°,a stability curve is used.39