船舶自由横動搖に關する理論

This paper deals with the free rolling of ship theoretically and experimentally, and the following results are obtained. (1) The free rolling of ship is made up of coupled oscillations of a horizontal transverse motion of its centre of gravity G with a rotational motion of ship about a longitudinal axis through G. And the horizontal motion is made up of two motions, the one being a damped oscillation and the other a damped translation, but the rotation simply a single damped oscillation. That is to say that, G, about the longitudinal axis through which the ship is rotating, translates transversely in the direction against the initial heeling, oscillating horizontally, and at last after the shift of a certain distance the motion is at rest. (2) C_0,the apparent centre of free rolling, which is the point having a minimum double amplitude of horizontal oscillation 2|ξ|_m_0 among the points in the middle line of the ship, is at a distance Y_0 below G. For box-shaped model ship, a ratio Y_0/d, where d is a draught of ship, has a value of about 0.08,and a ratio 2|ξ|_m_0/d increases as the initial angle of h el θ_0 increases and has a value of 0.03 at θ_0=35°. And these calcn'ated valnes of Y_0 and 2|ξ|_m_0 are in agreement with the experimental results. (3) The actual amplitudes of hor zontal oscillations of any point in the middle line of the ship are larger and more irregular than the calculated ones, but the direction and the amount of the horizontal translation calculated agree with the experimental results And D, a calculated distance of a horizontal shift of G between the time elapsed from the initial and the final instant of the motion, coincides perfectly with the experim ntal results. and D/d increases as 〓_0 increases and has a value of 0.9 at θ_0=35°. (4) A damping power α and a circular frequency ω in the free rolling of the ship are expressed as follows. [numerical formula] [numerical formula] where α_0 and ω_0 are a damp ing power and a circular frequency respectively in the free rolling of the ship, the horizontal motion of the centre of gravity of which are restrained. Therefore, C_α and C_ω are the effects of the horizontal motion on the free rolling, and the calculated C_α and C_ω agree with the experimental results. For the box-shaped model ship, the calculated C_u/α, C_ω/ω^2 and (T_0-T)/T (where T and T_0 are w/ω and π/ω0 respectively) have the following values. C_α/α : 7%～4% in the range of θ_0=0°-35°. C_ω/o^2 : about 4% throughout the same range of θ_0 as above. (T_0-T)/T : about 2% throughout the same range of θ_0 as above. (5) If the effect of the horizontal motion on the free rolling should be neglected as small, the damping power α and the period T, which shall be greatly influenced by the rotational motion, are approximately expressed as follows. [numerical formula] [numerical formula] Namely, α is proportional to the resistance couple I_<10>h_1 and inversely proportional to the apparent moment of inertia (I+I_1h_I), but small affected by the form of the ship. T^2 is proportional to the apparent moment of inertia and inversely proportional to the weight of the ship W, the metacentric height h and the effect of the form G_3,where G_3 is a non-dimensional factor which is a functin of the form of the statical stability cu ve and the initial angle of heel θ_0. (6) By the facts that the calculated values of Y_0,2