Moment of inertia of waterplane (IT, IL)

The waterplane moments of inertia I_T and I_L are the second moments of the waterplane area about its longitudinal and transverse centroidal axes. I_T governs transverse stability through the metacentric radius BM = I_T / V, where V is the displaced volume; I_L governs longitudinal stability through BM_L = I_L / V and feeds the moment to change trim one centimeter. Both come from integrating the half-breadth offsets along the length: I_T scales with the cube of beam, so wide hulls gain transverse stability fast. They are pure geometric properties of the waterline shape at a given draft, recomputed at each waterline in the hydrostatic table.