横動搖に於ける船の重心の運動と波の有効傾斜に就いて
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概要
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This paper treats the rolling of a ship of a moderate size relative to the wave by a similar method as Prof. Kriloff^<(1)> did, but it is endeavoured to get a more accuracy for approximation, and several new results are obtained. At first the general equations of motion are deduced retaining the terms of order r_o/R compared to unit, but as these are too complicated for practical use, gentle waves are taken as a first approximation for analysis. Moreover, a simple ship form is taken instead of real one for the convenience of the deduction of practical formulae, i.e., the cylindrical form with the section of the load water plane, but the draft being modified so as to give the probable results. Important results are those : 1. Equation of motion of centre of gravity of a ship are written ; [numerical formula] where [numerical formula]. If θ is small, the 2nd terms of the right-hand sides can be neglected, and x_g and y_g are obtained as [numerical formula] these show that the path of C.G. of the ship is elliptic, major axis being vertical, and the motion is less as the C.G. lies higher. The draft is much more influential than breadth for this motion. 2. When the rolling is considerable such as in a synchronous one, 2nd terms of the right-hand sides of (1) are not negligible, and, by inserting θ=θ_osin(tω-δ), approximate solutions can be got. By these substitutions, a constant term [numerical formula] appears in both equations, positive in the first and negative in the second. The positive constant term in the first means a drifting force in the direction of wave propagation, though, in the second, the constant term only changes the origin of the vertical oscillation. This drifting force was shown by Dr. Suyehiro's experiment, ^<(1)> though owed to the quite different cause. By inspecting M. it will be seen that the drifting force is positive for a broad and shallow ship, and is negative for a narrow and deep one, which phenomena can be simply tested in the experimental tank. 3. By rejecting the terms of order [numerical formula], the equation for rolling is ; [numerical formula] where [numerical formula] Then the reduction coef. γ for the effective wave slope becomes [numerical formula]. If we put γ=1-Φ/m, Φ/b is calculated as follows ; [numerical formula] where [numerical formula] This result may be compared with the W. Froude's approximate formula^<(2)> which can be rewritten as [numerical formula] The formula (3) is applicable so far as β≦0・7,and is calculated for certain values of α, β, etc., and represented in Fig.3,4,and 5. These show that Φ/b becomes less as the C.G. rises, and this tendency increases as β becomes greater. This facts aceount for the heavy rolling of a top-heavy ship, and also for the unsafe of small ferry which serves on the inland sea where small but steep waves are liable to occur. 4. For a large rolling, the approximate solution for θ is inserted in the right-hand, then there appears constant negative term, which shows that the rolling is asymmetric and the inclination is greater on the weather-side than on the lee-side. These researches are only theoretical, and no cares are taken for the resistance due to wave, which is very important, but difficult to get. Yet, by using the above theoretical results, especially the reduction coef., the analysis of the experimental results will be very convenienced, and it will not be so difficult to study the true nature of the active resistance to rolling on the waves.
- 社団法人日本船舶海洋工学会の論文
- 1932-04-30