Principles of naval engineering - Historic Naval Ships Association

xPRINCIPLES OF NAVAL ENGINEERINGenZ.hOb30,000Zu20,000O%oH10.000Zo10 20 30ANGLE OF HEEL IN DEGREES'40 50 60 70MAXIMUM RIGHTING MOMENT- DEVELOPS AT 38'Figure 3-27. — Curve of righting moments.147.43The distance G3Z3 is the righting arm theship would have if the center of gravity hadrisen from G to G3 and this virtual rise of Gmay be computed from the formula:GG3= J-VReferring to the formula, loss in GZ=—sin . This formula is accurate for small anglesof heel only, due to the pocketing effect as theangle increases. In case several compartmentsor tanks have free surface, their surface momentsof inertia are calculated individuallyand their sum used in the correction for freesurface. The effect of a given area of looseliquid at a given angle of heel is entirely independentof the depth of the liquid in the compartment,as is apparent in the formula,b"^l12where the only factors are the dimensions ofthe surface and the displacement of the ship.The free surface effect is also independent ofthe free surface location in the ship, whetherit is high or low, forward or aft, on the centerlineor off, as long as the boundaries remainintact.The loss of metacentric height can obviouslycan be reduced by reducing the breadth of thefree surface, as bythe installation of longitudinalbulkheads. However, off-center flooding afterdamage then becomes possible, causing the shipto take on a permanent list and usually bringingabout a greater loss in stability than if thebulkhead were not present.The loss of GZ due to free surface is alwayslessened to some extent by pocketing. This isthe contact of the liquid with the top of the compartmentor the exposure of the bottom surfaceof the compartment, either of which takes placeat some definite angle and reduces the breadthof the free surface area. To understand howpocketing of the free surface reduces the freesurface effect, study figure 3-29. Part A showsa compartment in which the free surface effectis not influenced by the depth of the loose water.The compartment shown in part B, however, containsonly a small amount of water; when theship heels sufficiently to reduce the waterline54