Ship Dynamics and Seakeeping
Motions and response
Seakeeping treats the ship as a rigid body with six degrees of freedom: surge, sway, heave, roll, pitch and yaw. Each mode has a natural frequency set by mass (including added mass) and restoring force. Roll is lightly damped and dominated by GM: approximately T_φ = 2π·k_x/√(g·GM), with roll radius of gyration k_x typically 0.35B–0.40B. Heave and pitch periods depend mainly on draft and length. Response amplitude operators give motion per unit wave amplitude against encounter frequency, and resonance occurs when encounter frequency matches a natural frequency.
Traps
Use encounter frequency, not absolute wave frequency, when the ship is underway. A larger GM shortens the roll period but stiffens the ship and increases accelerations. Parametric roll, broaching and slamming are nonlinear and not captured by linear RAOs. Verify IMO intact stability criteria, including the weather criterion, rather than relying on GM alone. Added mass and damping vary with frequency.
Worked example
B = 20 m, k_x = 0.35B = 7.0 m, GM = 1.0 m. T_φ = 2π × 7.0/√(9.81 × 1.0) = 43.98/3.13 = 14.0 s. Rule of thumb: roll periods of 10–20 s are typical for medium ships, and a period close to the encountered wave period signals possible synchronous roll.