PRINCIPLES OF NAVAL ENGINEERING 



For practical work. BM' is usually substituted 

 for GM' since they are both large and the dif- 

 ference between them is relatively small. When 

 this is done, howver, MTI is called the approxi- 

 mate moment to change trim one inch. This 

 value may often be found as a curve in the curves 

 of form (fig. 3-25). If not, the approximate 

 moment to change trim one inch may be calcu- 

 lated from 



MTI = 



BM' X W 

 12 L 



CALCULATION OF CHANGE OF TRIM 



The movement of weight aboard ship in a 

 fore-and-aft direction produces a trimming 

 moment. This moment is equal to the weight 

 multiplied by the distance moved. The change 

 of trim in inches may be calculated by dividing 

 the trimming moment by the moment to change 

 trim one inch: 



change of trim 



w X t 

 = MTI 



The direction of change of trim is the same 

 as that of weight movement. If we are using mid- 

 ships as our axis of rotation, the change in draft 

 forward equals the change in draft aft. This 

 change of draft forward or aft is one-half the 

 change of trim; for example, for a change of 

 trim by the stern the after draft increases the 

 same amount the forward draft decreases, that 

 is, one-half the change of trim. The reverse 

 holds true for a change of trim by the bow. 



Example: If 50 tons of ammunition are moved 

 from approximately 150 feet forward of the 

 center of flotation to approximately 150 feet aft 

 of the center of flotation (300 feet), what are the 

 new drafts? 



draft fwd= 19 feet 9 inches 



draft aft= 20 feet 3 inches 



mean draft = 20 feet 



trimming moment = 50 x 300 = 15, 000 foot-tons 



moment to change trim one inch = 1940 foot- 

 tons, from the following calculation: 



MTI 



BM' X W _ 1150 xll.800 



12 L 



12 X 582 



1940 foot-tons 



(BM' from curve in figure 3-25) 



. f . ■ - 15,000 _o . , , ^^ 

 change of trim- -8 inches by the stern 



1940 



change of draft — 4 inches fwd, 4 inches aft 



new draft fwd= 19 feet 5 inches 

 new draft aft = 20 feet 7 inches 



LONGITUDINAL WEIGHT ADDITION 



The addition of a weight either directly above 

 or below the center of flotation will cause an 

 increase in mean draft but will not change trim. 

 All drafts will change by the same amount as 

 the mean draft. The reverse is true when a 

 weight is removed at the center of flotation. 



To determine the change in drafts forward 

 and aft due to adding a weight on the ship, the 

 computation is in two steps. First, the weight is 

 assumed to be added at the center of flotation. 

 This increases the mean draft and all the drafts 

 by the same amount. The increase is equal to 

 the weight added, divided by the tons-per-inch 

 immersion. With the ship at its new drafts, the 

 weight is assumed to be moved to its ultimate 

 location. Moving the weight fore and aft produces 

 a trimming moment and therefore a change in 

 trim which is calculated as previously described. 



FLOODING EFFECT DIAGRAM 



From the flooding effect diagram of the 

 ship's Damage Control Book it is possible to 

 obtain the change in draft fore and aft due to 

 solid flooding of a compartment. The weight of 

 water to flood specific compartments is given 

 and trimming moment produced may be com- 

 puted, as well as list in degrees which may be 

 caused by the additional weight. Additional in- 

 formation on the flooding effect diagram can be 

 obtained from Chapter 9880 of the Naval Ships 

 Technical Manual. 



EFFECT OF TRIM ON TRANSVERSE 

 STABILITY 



The curves of form prepared for a ship are 

 based on the design conditions, i.e., with no 

 trim. For most types of ship, so long as trim 

 does not become excessive, the curves are still 

 applicable, and may be used without adjustment. 



When a ship trims by the stern, the trans- 

 verse metacenter is slightly higher than indi- 

 cated by the KM curve, because both KB and 

 BM increase. The center of buoyancy rises be- 

 cause of the movement of a wedge of buoyancy 

 upward. The increased BM is the result of an 

 enlarged waterplane as the ship trims by the 

 stern. 



58 



