Chapter S-STABILITY AND BUOYANCY 



Maximum righting arm AB. 



Angle of maximum righting arm at A. 



Range of stability 20° to 50°. 



Total dynamic stability is represented 



by the lined area. 



The ship will have a permanent list at 20 ° 

 ch is the angle where B is under G, inclining 

 1 equals original righting arm, cosine curve 

 sses original GZ curve, and residual right- 

 arm is zero. In a seaway the ship will roll 

 ut this angle of list. If it rolls farther to the 

 ed side, a righting moment develops which 

 is to return it toward the angle of list. If 

 •oils back towards the upright, an upsetting 

 nent develops which tends to return it to- 

 ■d the angle of list. The upsetting moment 

 ;ween ° and the angle of list) is the differ- 

 e between the inclining and righting moments. 



GONAL WEIGHT SHIFT 



A weight may be shifted diagonally, so that 

 noves up or down and athwartship at the 

 le time, or by moving one weight up or down 

 another athwartship. A diagonal shift should 

 treated in two steps; first by finding the ef- 

 ; on GM and stability of the vertical shift, 

 second, by finding the effect of the hori- 

 tal movement. The corrections are applied 

 jreviously described. 



EFFECTS OF WEIGHT CHANGES 



The additional removal of any weight in a 

 D may affect list, trim, draft, displacement, 



and stability. Regardless of where the weight 

 is added (or removed), when determining the 

 various effects it should be considered first 

 to be placed in the center of the ship, then 

 moved up (or down) to its final height, next 

 moved outboard to its final off-center location, 

 and finally shifted to its fore or aft position. 

 Assume that a weight is added to a ship so 

 that the list or trim is not changed, and G will 

 not shift. The first thing to do is find the new 

 displacement, which is the old displacement 

 plus the added weight: 



New displacement = W + w tons 



where 



W = old displacement (tons) 

 w = added weight (tons) 



With the new value of displacement, enter the 

 curves of form and on the displacement curve 

 find the corresponding draft, which is the new 

 mean draft. Figure 3-25 shows typical displace- 

 ment and other curves generally referred to 

 as curves of form. 



If the change in draft is not over 1 foot, the 

 procedure can be reversed. Find the tons-per- 

 inch immersion for the old mean draft from 

 the curves of form, divide the added weight 

 (in tons) by the tons-per-inch immersion in 

 order to get the bodily sinkage in inches, and 

 add this bodily sinkage to the old mean draft 

 to get the new mean draft. Using the new mean 

 draft, enter the curves of form and find the 

 new displacement. 





10 20 



30 40 



50 



60 



70 80 90 



ANCLE OF HEEL IN DEGREES 



Figure 3-23.— Cosine curve superimposed on original stability curve. 



49 



147.39 



