PRINCIPLES OF NAVAL ENGINEERING 



Example : Add four gun mounts topside to a 

 ship with the curves of form shown in figure 

 3-25. Assume an initial KG of 24.5 feet. Assume 

 that the gun mounts weigh 28 tons each and that 

 their center of gravity is located 48 feet above 

 the keel. What is the effect on stability? 



1. New displacement = W+ w= 11,500+ (4 x 

 28) =11,612 tons. 



2. New mean draft = 19.7 feet (fig. 3-25). 

 wz 



3. GGi = 



W+ w 



w= 4 X 28= 112 tons 

 z =48 - 24.5 =23.5 feet 

 112 X 23.5 



GGi = 



11,612 



0.23 feet 



4. KG^ = 24,50 +0.23 = 24.73 feet. 



5. New KMj = 28.4 feet (fig. 3-25). 



6. New GiMi = KM^ - KGi = 28.4 

 3.7 feet. 



- 24.7= 



7. The values for the angles (0 °— 70°) are 

 taken from the cross curves for 11,612 

 tons displacement (fig. 3-14). KA is 20 feet. 

 Corrections are made for AGi x sini? = 

 (24.73 - 20) sin(9=4.73 sinS. The correc- 

 tions are applied to the curve (fig. 3-26) 

 as previously explained. Figure 3-26 

 shows the curve of righting arms cor- 

 rected for weight addition, 



HORIZONTAL WEIGHT CHANGES 



In the previous example of weight addition, 

 suppose the gun mounts are located with their 

 center of gravity 29 feet to starboard of the 

 centerline and the weight is moved athwartship 

 to its final off-center location. The shift in G 

 may be found by using the proper formula, mak- 

 ing the required corrections, and applying the 

 corrections to the curve in figure 3-26. This 

 gives a correct curve of righting arms. To 

 obtain a curve of righting moments, the righting 

 arms are multiplied by the new displacement 

 (W+w) = 11,612 tons, and plotted in figure 3-27. 



WEIGHT REMOVAL 



The results of a weight removal are com- 

 puted by using the previous procedure, the only 



difference being that most of the operations 

 and results will be found just the reverse of 

 those which relate to adding a weight. 



EFFECTS OF LOOSE WATER 



When a tank or a compartment in a ship is 

 partially full of liquid that is free to move as 

 the ship heels, the surface of the liquid tends to 

 remain level. The surface of the free liquid is 

 referred to as free surface . The tendency of the 

 liquid to remain level as the ship heels is re- 

 ferred to as free surface effect . The term loose 

 water is used to describe liquid that has a free 

 surface; it is not usedtodescribe water or other 

 liquid that completely fills a tank or compart- 

 ment and thus has no free surface. 



FREE SURFACE EFFECT 



Free surface in a ship always causes a re- 

 duction in GM with a consequent reduction of 

 stability, superimposed on any additional weight 

 which would be caused by flooding. The flow of 

 the liquid is an athwartship shift of weight which 

 varies with the angle of inclination. Wherever 

 free surface exists, a free surface correction 

 must be applied to any stability calculation. This 

 effect may be considered to cause a reduction in 

 a ship's static stability curve in the amount of 



4i-x sin^, due to a virtual rise inG 



where 



i = the moment of inertia of the surface of 

 water in the tank about a longitudinal axis 

 through the center of area of that surface 

 (or other liquid in ratio of its specific 

 gravity to that of the liquid in which the 

 ship is floating)^ 



V = existing volume of displacement of the 

 ship in cubic feet. For a rectangular com- 

 partment, i may be found from 



b^i 



12" 



where 



b= athwartship breadth of the free surface 



(with the ship upright) in feet 

 1= fore-and-aft length of the free surface in 



feet 



It is usual to assume all liquids are salt water, and 

 thus neglect density, unless very accurate determina- 

 tions are required. 



52 



