Principles of naval engineering - Historic Naval Ships Association

CHAPTERSSTABILITY AND BUOYANCYThis chapter deals with the principles ofstability, stability curves, the inclining experiment,effects of weight shifts and weight changes,effects of loose water, longitudinal stability andeffects of trim, and causes of impaired stability.The damage control aspects of stability arediscussed in chapter 4 of this text.PRINCIPLES OF STABILITYA floating body is acted upon by forces ofgravity and forces of buoyancy. The algebraicsum of these forces must equal zero if equilibriumis to exist.Any object exists in one of three states ofstability: stable, neutral, or unstable. We mayillustrate these three states by placing threecones on a table top, as shown in figure 3-1.When cone A is tipped so that its base is offthe horizontal plane, it tends, up to a certainangle of inclination, to assume its originalposition again. Cone A is thus an example of astable body— that is, one which tries to attainits original position through a specified rangeof angles of inclination.Cone B is an example of neutral stability.When rotated, this cone may come to rest atany point, reaching equilibrium at some angle ofinclination.Cone C, balanced upon its apex, is an exampleof an unstable body. Following any slight inclinationby an external force, the body willcome to rest in a new position where it willbe more stable.From Archimedes' law, we know that anobject floating on or submerged in a fluid isbuoyed up by a force equal to the weight of thefluid it displaces. The weight (displacement)of a ship depends upon the weight of all parts,equipment, stores, and personnel. This totalweight represents the effect of gravitationalforce. When a ship is floated, she sinks intothe water until the weight of the fluid displacedby her underwater volume is equal to the weightof the ship. At this point, the ship is in equilibrium—thatis, the forces of gravity (G) andthe forces of buoyancy (B) are equal, and thealgebraic sum of all forces acting upon the shipis equal to zero. This condition is shown inpart A of figure 3-2. If the underwater volumeof the ship is not sufficient to displace anamount of fluid equal to the weight of the ship,the ship will sink (part B of fig. 3-2) becausethe forces of gravity are greater than theforces of buoyancy.The depth to which a ship will sink whenfloated in water depends upon the density ofthe water, since the density affects the weightper unit volume of a fluid. Thus we may expecta ship to have a deeper draft in fresh waterthan in salt water, since fresh water is lessdense (and therefore less buoyant) than saltwater.Although gravitational forces act everywhereupon the ship, it is not necessary to attempt toconsider these forces separately. Instead, wemay regard the total force of gravity as a singleresultant or composite force which acts verticallydownward through the ship's center ofgravity (G). Similarly, the force of buoyancymay be regarded as a single resultant forcewhich acts vertically upward through the centerof buoyancy (B) located at the geometric centerof the ship's underwater body. When a ship isat rest in calm water, the center of gravityand the center of buoyancy lie on the samevertical line.DISPLACEMENTSince weight (W) is equal to the displacement,it is possible to measure the volume of the underwaterbody (V) in cubic feet and multiply thisvolume by the weight of a cubic foot of sea34