A Study of Ship Motion Stabilization 



tank investigations. We feel that the tank scale effect problem must be further 

 explored if passive anti-rolling tanks are to continue to be installed in seakeep- 

 ing basin ship models. We have attained better agreement than that shown in 

 Fig. 25 of the paper between our current weakly nonlinear theory and other ex- 

 perimental data. This better agreement is, however, not sufficiently good for 

 practical use. One further remark is perhaps justified and that is that detailed 

 space-time mappings of the free surface in a tank indicate that the fluid seldom 

 behaves in a fashion similar to either that in a U-tube or to a first mode stand- 

 ing wave. Evidently, considerable additional effort on the fluid dynamics of the 

 free-surface passive anti-rolling tank will be necessary. 



DISCUSSION 



S. Motor a 

 University of Tokyo 

 Tokyo, Japan 



I would like to make some short comments on the anti-pitching tank. As 

 Mr. Giddings has mentioned, the idea is to put openings at the bottom of fore or 

 aft peak tanks to let sea water come in and out in a 90 degree phase lag behind 

 the pitching motion resulting in a reduction of pitching motion. 



This problem was initiated by the Technical Research Laboratory of Hitachi 

 Shipbuilding Co. and was published in the fall, last year. In that paper, move- 

 ment of the water level in open tanks, installed at the bow and the stern, is ana- 

 lysed theoretically, and the pitching angle of a ship in regular waves, affected 

 by such tanks, is calculated. A model experiment with a model of a passenger 

 ship was conducted to check the calculation. Two tanks were installed; one at 

 the bow and one at the stern. The total water plane area of the tanks was 25 

 percent of the ship's water plane area. 



Results are as shown in Fig. 1, where a is the area of the openings at the 

 bottom of the tanks and A is the waterplane area of the tanks. About 45 percent 

 reduction at the maximum was attained. 



I treated the same problem and dealt mainly with the fundamental charac- 

 teristics of tanks with openings under the water line. 



At first, let us consider a tank with a vertical wall. In Fig. 2, suppose a 

 tank has openings of area a . Free surface area of the tank is A, the depth of 

 the openings is h , heaving of the tank is z, and elevation of tank water is i. 



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