PRINCIPLES OF NAVAL ENGINEERING 



a: 



2p tNCLINING ARM CURVE 



OLD RIGHTING ARM CURVE 



u, 



g 



H 

 X 

 O 



5 



2 w 



a - 



c 



3 



ANGLE OF HEEL IN DEGREES 



147.40 

 Figure 3-24.— New curve of static stability after correction for horizontal weight movement. 



VERTICAL WEIGHT CHANGES 



Assume that the weight added above is shifted 

 vertically on the ship's centerline to its final 

 height above the keel. This movement will 

 cause G to shift up or down. To compute the 

 vertical shift of G use the formula 



GGi = 



wz 



(W + w 



where 



GGi 

 w 

 z 



W 

 (W+ w) 



shift of G up or down, in feet 



added weight, in tons 



vertical distance w is added above 



or below original location of G, in 



feet 



old displacement, in tons 



new displacement, in tons 



This vertical shift must be added to or sub- 

 tracted from the original height of the center 

 of gravity above the keel. 



To do this, the original height KG must be 

 known: 



where 



KGi 

 KG 



KGi = KG + GGi 



new height of G above keel (in feet) 

 old height of G above keel ( in feet) 



GGl = shift of G from formula GGl = 



wz 



(W+ w) 



If the final position of the added weight is 

 below the original position of G, then GGj^ is 

 minus; if it is above, then GGi is plus. 



To find the new metacentric height, enter 

 the curves of form with the new mean draft 

 and find the height of the transverse meta- 

 center above the base line. This is KM^. The 

 new metacentric height is determined by the 

 formula. 



GiMi= KMi - KGl 



where 



GiMi= new metacentric 

 KMi = new KM 

 KGl = "^w KG 



height (in feet) 



With the new displacement (W + w), enter 

 the cross curves and pick out a new, uncorrected 

 curve of stability. Correct this curve for the 

 new height of the ship's center of gravity above 

 the base line. This is accomplished by finding 

 AGi (which is KGl minus KA) and subtracting 

 AGi X sin 6 from every vertical on the stability 

 curve, provided Gl is above A. If Gl is below 

 A, the values of AGi x sin 6 must be added to 

 the curve, as previously explained. The result- 

 ing curve of righting arms is now correct for 

 the loss of freeboard due to the added weight 

 and for the final height of the ship's center of 

 gravity resulting from weight addition. 



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