船舶の振幅半減衰動搖囘數に就いて
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概要
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The writer has been studying in the manner of expression of the damping properties of the rolling motion of ships and the method of analysis which is simple and is to be employed in various calculations, having just achieved some of the results as follows. In the general case of the curve of extinction to be expressed by an arbitrary function of amplitude θ as having an entire approximation the expression of the damping properties of the rolling motion of ships is considered to be appropriate as explained in the following sequence. (1) In order to express, of the first significance, the damping properties of the motion peculiar to hulls the number of swing fo the rolling to decrease to one-half amplitude μ is employed in the amplitude θ=10°. Furtheremore to express the degree of increase in the damping of the rolling for the augmentation of amplitude, (μ_2)/(μ_1), ratio of the number of swing for the rolling to decrease to one-half amplitude μ_2 and μ_1 in amplitude θ=20° and 10°is employed. (2) The value of these μ_2 and μ_1 can be obtained directly from the experimental result of the rolling motion. (3) The damping properties of the rolling motion among waves are expressed by maximum amplitude in synchronous rolling θ_<max> in the simplified imaginary standard condition on the utmost audacious assumption. In this case the damping forces among waves are taken for those in the still water and that which is learnt from Zimmermenn's study is taken for the standard condition of waves. (4) If the damping properties of the rolling motion of ships are expressed by the number of swing for the rolling to decrease to one-half amplitude μ in an arbitrary amplitude, μ is found from μ_1 and (μ_2)/(μ_1) as shown below ; [numerical formula] (5) The maximum amplitude in synchronous rolling among waves θ_<max> is found by graphic method from the following expression. [numerical formula] where {θ_w ; the slope of the surface trochoid γ ; the coefficient of the effective wave slope α_e, δ_e ; by using the above expression can be found μ_1 and (μ_2)/(μ_1).