Abstract
There are mutually many similar characters in heaving and pitching motion of a ship; namely, in her virtual mass, period, etc, but heaving's velocity, acceleration corresponds to pitching's amplitude, velocity, respectively. (1) For rate of increase of virtual inertia; Heaving: Δ_h=π/8B/h・2m/2m+1 Pitching: Δ_p=π/8B/h・2m/2m+3 where B: breadth, h: drought, C_w=m/(m+1); water-line coefficient. (2) For ships period, Heaving: T_h=2π√<h/g(1+Δ_h);> Pitching: T_p=2π√<h/g(1+Δ_p)> where g: gravitational acceleratioin. So that each value is almost equal, but for pitching are slightly less than those of for heaving. (3) For maximum resonanced amplitude: Heaving, [numerical formula] Pitching, [numerical formula] where, damping force is assumed to be proportional to square of velocily of motion, γ_h, γ_p: effective coefficient, its value is usually about 1/4〜1/3, L: ships length, β_h=gTh/2πu, β_p=gTp/2πu: resonance wave-age, u is wind velocity, δ0e-β_<h^2>: resonanced wave steepness. When a ship is rolling in confused seas, criical amplitude, velocity, acceleration are approximately [numerical formula] where [numerical formula] and n=1 forZ^^-; n=0, for Z and φ, n=-1 for Z and φ, n=-2, for φ respectivety. N is numbers of oscillations. Φ(-1) has maximum value o about 1/2, for β≒1/2 which implies that there may occur very heavy up-and-down motion.
