This paper deals with the designing method of anti-rolling tanks of three types as shown in Fig. A on the theoretical basis.
The main principle for design is that the rolling of ship with tank is surely less than that of the ship with tank checked, so far as the period of wave is less than that of the ship itself.
As for the Frahm's type, the theory given by Woollard is adopted, and therefrom the designing method is developed. The procedure is as follows: let the curve of
m(=amplitude of rolling/max. effective wave slope) be drawn with the abscissa
e(=period of ship/period of wave) for the rolling with tank open and checked respectively as in the figure on page 10. Then the three conditions are obtained to find the three parameters,
i. e. the size and the period of the tank, and the damping in the oscillation of tank water. The conditions are,
1. The value of
e, for which the max.
m occurs on
e>1 side, coincide with that, in which
mμ curve intersects with
mμ=0 curve as
M' in the figure.
2. The amplitude at
M' is equal to that at
e=1, that is,
m1'=
mo.
3. The amplitude of oscillation in tank water corresponding to this period of wave for
M' must be a given value.
The three parameters are found so as to satisfy these conditions, and the results of calculations are given in Fig. 6, from which, if the height of the tank is given from the constructional stand point (
n=max. amplitude of oscillation of tank water/max. effective wave slope), the period(
f=period of ship/period of tank), the size (μ=% of loss of metacentric height due to the free sur- facesof the tank) and the damping(
bt=2×extinction coef. of free oscillation in tank/π) can be easily found with the max. rolling angle(
m=max. rolling angle/max. effective wave slope).
In this method, the effect of the position of the tank is neglected as secondary.
For Foerster's two types, the new theory is established in each case, but their actions are quite similar, only differing in the resistance to the motion of water in tank. The rolling angle for variable
e is shown in Fig. 7, where μ means the same as above. From this figure, it is observed that the max. rolling occurs at
e=1 so far as
e_??_1, and by this fact, the relation between the maximum rolling angle and μ is obtained and given in Fig. 8. The resistance to the motion of water in tank affects the curve of Fig. 8. very slightly, and is safely neglected for designing purpose. As for the size of the hole which connects the tank with open sea, its determination is much affected by the resistance, and for that purpose the formula is given for the known value of the resistance, which must be experimentally determined in each practical case.
Lastly, the three types are compared, and the author's opinion is that the Frahm's type is better than the others on the practical point of view, if it is suitably designed.
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