On the Rolling of a Ship on a Billow : Fluctuation of Apparent Ship-Weight

Abstract

In this paper, we direct our attention to fluctuation of the apparent weight of a ship who rolls among regular heavy waves. Fluctuation is usually ignored because of the supposition that waves are gentle. But it is considerable in amount is waves are heavy. It exerts significant effects upon the ship rolling and brings interesting features on her behavior. We examine the features experimentally by model tests on a navipendular or on water tanks and theoretically by solving the rolling equation of the type [numerical formula]. In this equation, θ_a = the relative angle of heel, K = the coefficent of damping, ω_0 = the natural circular frequency, M, β = the characteristic coefficients representing non-harmonic character and Mω^2sin ωt=the external force. To solve approximately the equation, we make use of the averaging method under the assumption that the solution may be expressible in a form of θ_a = A sin (ωt-ψ) + B sin (ω't-ψ').