船舶の動搖造波抵抗に関する研究 : 其の一T.H.Havelockの方法の一解釋と其の擴張

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In the Dr. T.H. Havelock's method on computation of a wave height at a fluid surface produced by a periodic motion of a doublet D in two dimensions, a supplementary velocity potential φ_1 in the first approximation, with which the conditions at the free surface are satisfied, has a term representing a image doublet D refered to the free surface. φ_1 does not satisfy the condition in vicinity of D, but gives disturbance. The surface of a body moving in the fluid may be replaced by a suitable arrangement of doublets on the periphery. When considering a body tied up in one sheet with its image refered to a surface which will be supposed to be a free surface henceforth, and giving a required normal velocity distribution along the lower half of the periphery, φ_1 corresponding to the motion, now, does not contain a term like D which contributes to the bonndary conditions. And disturbance at the boundary produced by φ_1 will be moderately decreased. In this view and after Dr. Havelock, if φ_0 be a velocity potential for the motion of the fluid, the free surface of which is neglected for a while, and if φ=φ_0+φ_1,the conditions for the free surface to be sutisfied by φ are. [numerical formula] where the axis x is on the free surface and the y vertical upwards ; t time, y acceleration due to gravity, η the displacement of the free surface, 2π/σ the period of the motion, and μ a coefficient of the resistance proportional to the velocity. The required φ_1 & η are [numerical formula] in which the progressive waves are included as follows ; [numerical formula] where -x_1 & x_2 (-x_1<x_2) are the coordinates at which the contour of the body cuts the x-axis, and the double signs correspond to x>ξ and x<ξ respectively. φ_0 is often obtainable with such the comformal transformation, easier than to findi the distribution of doublets in the Dr. Havelock's method. This method may be readily extended for the stesdy motion or the three dimensional one.
社団法人日本船舶海洋工学会の論文

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菱田敏男
大阪工業専門学校

船舶の動搖造波抵抗に関する研究 : 其の一T.H.Havelockの方法の一解釋と其の擴張

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