Roll Angle of a Ship: Simple Equation Explained

[Tone L]

I have been on the hunt looking for a precise equation that gives you the angle that a ship is displaced along its x-axis (roll). There is a somewhat simple equation:Roll angle (Θ) : Θ = Acos( ωt+ φ)------where A is the amplitude of the wave, ω is the frequency and φ is the phase chage.

So what would time be??

 

[SteamKing]

I have been on the hunt looking for a precise equation that gives you the angle that a ship is displaced along its x-axis (roll). There is a somewhat simple equation:Roll angle (Θ) : Θ = Acos( ωt+ φ)------where A is the amplitude of the wave, ω is the frequency and φ is the phase chage.

So what would time be??

The rolling motion of a ship is generally a non-linear phenomenon. For small angles, the rolling motion may be linearized approximately so that it corresponds roughly to simple harmonic motion, like what a pendulum experiences when it is disturbed from the equilibrium position.

I don't know where you obtained the equation in your post, but A is generally not the amplitude of the incident wave. What this equation is telling you is that the roll angle of the vessel is periodic in time, with a certain amplitude of roll, frequency, and phase w.r.t. some other datum.