The motion of the liquid in partially filled internal tanks reduces the hydrostatic stability of the floating structure.

As the liquid densities in the internal tanks may differ from the external water density, the definition of the metacentric height for a free-floating body with internal tanks is slightly different from that discussed in Small Angle Stability. The coefficients of the hydrostatic stiffness matrix are employed instead.

The principal axes are defined by

(3–43)

where is the angle between the principal X'-axis and the positive X-axis measured counterclockwise in the X-Y plane of the FRA.

The longitudinal and transverse metacentric heights are defined as

(3–44)

where ρ is the water density, and is the buoyant volume due to the displacement of external water (see Equation 3–1). The righting moment is defined by where the small angle β is indicated in Figure 3.1: Metacenter of a Free-Floating Body.

From Equation 3–44 and Equation 3–39, the reduction in the stability of the structure with internal tanks is proportional to the liquid surface area moment about the center of floatation of each tank. The large fuel and fresh water tanks of a ship may be distributed into the port, center and starboard compartments to reduce the liquid surface effect on the transverse stability. Each watertight compartment should be treated as a separate internal tank in the analysis.