A Survey of Ship Motion Stabilization 



Appendix 



EQUATIONS OF MOTION FOR ANTI- PITCHING TANK 



With the recent interest in passive anti-roll tanks, it is of interest to spec- 

 ulate on anti-pitching tanks. If, for instance, the forepeak tank of a ship were 

 somewhat enlarged and fitted with large openings at the bottom, the surging of 

 water in and out as the ship and waves interact might reduce pitching. Refer- 

 ence 56 reports on one special case in this regard. The tank involved was in 

 the stern of a slender double-ended ship form. Not enough data is presented to 

 compare with and without tanks, but the influence of the size of the tank openings 

 on the pitch period is presented. 



Figure 32 shows, in schematic form, the geometry of a bow tank open to the 

 sea at the bottom. The equations of motion, assuming uncoupled pitch and heave 

 for the "unstabilized" ship, have been derived using the Lagrangian formulation. 

 Linearizing assumptions include all the usual ones in regard to small motions 

 and linear damping. The tank geometry is assumed to be such that the area of 

 the tank free surface does not change as the tank water level changes. It is also 

 assumed that added mass terms and other coefficients of the ship are constants. 



Fig. 32 - Sketch of coordinate system 



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