Heave

Heave is the vertical translational motion of a ship along its z-axis, one of the three translational rigid-body modes (surge, sway, heave). Its linear equation of motion is (m + a_33) z-double-dot + b_33 z-dot + c_33 z = F_3(t), where a_33 is heave added mass, b_33 heave radiation damping, and c_33 = rho g A_w the restoring coefficient set by the waterplane area A_w. The undamped natural heave period is 2 pi times the square root of (m + a_33) over c_33. Heave couples strongly with pitch, and large heave near resonance drives vertical accelerations, deck wetness, and slamming.