Heeling moments

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Heeling Moments

Heeling moments are moments (a force x distance), about the longitudinal axis; transverse forces which have a tendency to induce roll (heel). The investigation of heeling moments are an important consideration to a vessels stability.



Heeling moments can be internal or intrinsic to a vessel, such as when the TCG and TCB are not aligned at 0 degrees inclination. They may be environmentally induced, by weather or waves. Heeling moments may also be induced by a ships operation, i.e., from working cranes or towing.

  • Constant: A moment which is unchanged by the heel angle of the vessel; such as by an external force.
  • Varying with the cosine: A force whose magnitude is height dependent will decreases as the vessel heels (such as wind loads), as the point of application will approach the waterline (or the exposed face obliques away). The moment can be calculated at varying angles of heel as;
HMupright x cosine (heel angle)
  • Defined: Often, heeling moments arise from a complex interaction of forces, such as from thrusters, monitors, and drivelines working simultaneously. Heeling moments will be derived mathematically, considered for the largest value, or interpolated from a number of output points.


For submarines, the centre of buoyancy does not change much with angle of heel (it is fixed by the submergence of the entire hull and the cylindrical shape common to modern subs), thus heeling moments are primarily a matter of weight distribution. The VCG should be kept below the VCB of the submarine, as close to centreline as possible, ensuring a righting tendency.


Some common induced heeling moments are;

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