Experimental Data on N-coefficient for Rolling Resistance of Ship Models without Bilge Keels (I)

Abstract

Experimental data are presented in this paper. The experiments were worked out by many students of our University in these several years. Rolling resistance of ship models without bilge keels were measured. Four models are related to the present report. The particulars and the test conditions are tabulated in Tables 1-4. The conditions count 220 in total. Together with the data reanalysed from the previous experiments on a cargo ship and an oil tanker, which had been presented in the Journal No.105 of the Society, a series of experiments on general ship form has been got through. In this report, the N-coefficient means N=Δθ/θ_m^2, where Δθ=angle of extinction in degrees due to resistances other than frictional one, θ_m=mean angle of roll in degrees. Δθ is obtained by deducing an angle of extinction due to frictional resistance from a total resistance measured. Frictional one can be calculated by Dr. Kato's formula. The results anaylsed are illustrated in Figs. 1-4. The nomenclatures used are lined up at Section 2. We may draw the following conclusions from these illustrations : 1) N is roughly independent of draft. 2) NZ^n of a particular model is a function of KG/D only. The mean line of NZ^n are superposed in (a) of Fig.6. In this figure, the reanalysed data of the previously reported models are added. 3) They have the minimum values without 0.7-0.8 of KG/D. Heavy curves signify the usual range of KG/D in actual ships. 4) The power index n is a function of Z, which coincides with the Holodilin data. [(b) in Fig.6]. 5) Also it depends on Z only, so long as the present models are concerned. That is to say, the n-curve in (b) is common over the six models. (c) in the same figure is the cross-section at particular KG/D, which is based on the abscissa of C_ν (at d/B=0.4). 6) NZ^n takes the minimum values at about C_ν=0.75. For models finer than this C_ν-value, that is for sharper bottom, NZ^n gets large rapidly. But for ones otherwise it is almost horizontal. The foregoings are data at θ_m=15°. Δθ at θ_m=10° or 20° are plotted against the former in Fig.5. 7) Δθ_<20°> are rather troublesome. But Δθ_<10°> are nearly linear with Δθ_<15°>, and about 2/3 of Δθ_<15°>. In order words, N_<10°> is nearly 1.5 times of N_<15°>. Finally, we add that it may be substituted for N of actual ships without bilge keels by the present data because frictional resistance of actual ships is negligibly small.