Added mass

Added mass is the apparent increase in a body’s mass caused by the surrounding fluid it must accelerate when the body accelerates. In ship motions it appears in each equation of motion as an extra inertia term, written a_ij, so the heave equation reads (m + a_33) z-double-dot + b_33 z-dot + c_33 z = F(t). It is frequency-dependent in a free surface because the body radiates waves, and is found from potential-flow radiation solutions via strip theory or panel (boundary element) methods. For a deeply submerged circular cylinder the added mass per unit length equals the displaced fluid mass, rho times pi r squared. Added mass lengthens natural periods of heave, pitch, and roll.