Pitch (motion)

Pitch is the rotational motion of a ship about its transverse (y) axis, the angular bow-up, bow-down oscillation. Its linear equation is (I_55 + a_55) theta-double-dot + b_55 theta-dot + c_55 theta = M_5(t), where I_55 is the pitch mass moment of inertia, a_55 the pitch added inertia, b_55 radiation damping, and the restoring c_55 = rho g times the longitudinal waterplane inertia, equal to displacement times g times the longitudinal metacentric height GM_L. The pitch gyradius k_yy is about 0.24 to 0.26 L. Pitch couples with heave, is well damped through wave radiation, and governs vertical bow accelerations, slamming, and added resistance in head seas.