艦船の横動搖試驗成績の新解析法

抄録

The rolling of a ship up to large angles of inclination in still water may nearly be expressed by
d²θ/dt²+2αsdθ/dt+λs²k²θ=0,
where λs²=Wh/I; W=the displacement; h=the me acentric height; I_s the apparent momentof inertia at any amplitude; k=the metacentric factor; ∫^θ2_-θ12αI_sdθ/dtdθ=the actualenergy lost per swing. Let k_i²=2E_i/Whθ_i², E_i being the dynamical stability at an inclinationθ_i, then we obtain
k²=k₁²θ₁²-k₂²θ₂²/θ₁²-θ₂² and 1-e-2α_sπ/√λ_s2k2-α_s²=θ₁²-θ₂²/θ₁²
If we know the successive amplitudes and the corresponding periods by experiments, we shall have the variation of the apparent moment of inertia in terms of amplitudeby the formula
I_s/I₀=T_s²/T₀²{k²-(α_s/λ_s)²},
where I₀ and T₀ are the apparent moment of inertia and the period of a single rollrespectively when the ship rolls to very small angles. It was found from the experimentalresults that the apparent moment of inertia increases with the amplitude even thoughthe period of roll decreases, and that no theoretical formulae neglecting its variationgive a correct value of period for any specified amplitude, particularly for ships fittedwith deep bilge keels.