Principles of naval engineering - Historic Naval Ships Association

wPRINCIPLES OF NAVAL ENGINEERINGExample : Add four gun mounts topside to aship with the curves of form shown in figure3-25. Assume an initial KG of 24.5 feet. Assumethat the gun mounts weigh 28 tons each and thattheir center of gravity is located 48 feet abovethe keel. What is the effect on stability?1. New displacement = W+ w= 11,500+ (4 x28) =11,612 tons.2. New mean draft = 19.7 feet (fig. 3-25).wz3. GGi = W+w= 4 X 28= 112 tonsz =48 - 24.5 =23.5 feet112 X 23.5GGi = 11,6120.23 feet4. KG^ = 24,50 +0.23 = 24.73 feet.5. New KMj = 28.4 feet (fig. 3-25).6. New GiMi = KM^ - KGi = 28.43.7 feet.- 24.7=7. The values for the angles (0 °— 70°) aretaken from the cross curves for 11,612tons displacement (fig. 3-14). KA is 20 feet.Corrections are made for AGi x sini? =(24.73 - 20) sin(9=4.73 sinS. The correctionsare applied to the curve (fig. 3-26)as previously explained. Figure 3-26shows the curve of righting arms correctedfor weight addition,HORIZONTAL WEIGHT CHANGESIn the previous example of weight addition,suppose the gun mounts are located with theircenter of gravity 29 feet to starboard of thecenterline and the weight is moved athwartshipto its final off-center location. The shift in Gmay be found by using the proper formula, makingthe required corrections, and applying thecorrections to the curve in figure 3-26. Thisgives a correct curve of righting arms. Toobtain a curve of righting moments, the rightingarms are multiplied by the new displacement(W+w) = 11,612 tons, and plotted in figure 3-27.WEIGHT REMOVALThe results of a weight removal are computedby using the previous procedure, the onlydifference being that most of the operationsand results will be found just the reverse ofthose which relate to adding a weight.EFFECTS OF LOOSE WATERWhen a tank or a compartment in a ship ispartially full of liquid that is free to move asthe ship heels, the surface of the liquid tends toremain level. The surface of the free liquid isreferred to as free surface . The tendency of theliquid to remain level as the ship heels is referredto as free surface effect . The term loosewater is used to describe liquid that has a freesurface; it is not usedtodescribe water or otherliquid that completely fills a tank or compartmentand thus has no free surface.FREE SURFACE EFFECTFree surface in a ship always causes a reductionin GM with a consequent reduction ofstability, superimposed on any additional weightwhich would be caused by flooding. The flow ofthe liquid is an athwartship shift of weight whichvaries with the angle of inclination. Whereverfree surface exists, a free surface correctionmust be applied to any stability calculation. Thiseffect may be considered to cause a reduction ina ship's static stability curve in the amount ofwhere4i-x sin^, due to a virtual rise inGi = the moment of inertia of the surface ofwater in the tank about a longitudinal axisthrough the center of area of that surface(or other liquid in ratio of its specificgravity to that of the liquid in which theship is floating)^V = existing volume of displacement of theship in cubic feet. For a rectangular compartment,i may be found fromwhereb^i12"b= athwartship breadth of the free surface(with the ship upright) in feet1= fore-and-aft length of the free surface infeetIt is usual to assume all liquids are salt water, andthus neglect density, unless very accurate determinationsare required.52