Principles of naval engineering - Historic Naval Ships Association

PRINCIPLES OF NAVAL ENGINEERINGa:2p tNCLINING ARM CURVE OLD RIGHTING ARM CURVEgHXO5u,2 wANGLE OF HEEL IN DEGREESa -c3147.40Figure 3-24.— New curve of static stability after correction for horizontal weight movement.VERTICAL WEIGHT CHANGESAssume that the weight added above is shiftedvertically on the ship's centerline to its finalheight above the keel. This movement willcause G to shift up or down. To compute thevertical shift of G use the formulawhereGGiwzW(W+ w)GGi =wz(W + wshift of G up or down, in feetadded weight, in tonsvertical distance w is added aboveor below original location of G, infeetold displacement, in tonsnew displacement, in tonsThis vertical shift must be added to or subtractedfrom the original height of the centerof gravity above the keel.To do this, the original height KG must beknown:whereKGiKGKGi = KG + GGiG above keel (in feet)new height ofold height of G above keel ( in feet)wzGGl = shift of G from formula GGl =(W+ w)If the final position of the added weight isbelow the original position of G, then GGj^ isminus; if it is above, then GGi is plus.To find the new metacentric height, enterthe curves of form with the new mean draftand find the height of the transverse metacenterabove the base line. This is KM^. Thenew metacentric height is determined by theformula.whereGiMi= KMi - KGlGiMi= new metacentricKMi = new KMKGl = "^w KGheight (in feet)With the new displacement (W + w), enterthe cross curves and pick out a new, uncorrectedcurve of stability. Correct this curve for thenew height of the ship's center of gravity abovethe base line. This is accomplished by findingAGi (which is KGl minus KA) and subtractingAGi X sin 6 from every vertical on the stabilitycurve, provided Gl is above A. If Gl is belowA, the values of AGi x sin 6 must be added tothe curve, as previously explained. The resultingcurve of righting arms is now correct forthe loss of freeboard due to the added weightand for the final height of the ship's center ofgravity resulting from weight addition.50