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Atwood's formula

B1. Naval Architecture

Definition

Geometric formulation of the righting arm via wedge transfer of buoyancy.

Atwood’s formula gives the righting arm GZ at large heel angles, where the metacenter no longer holds, by accounting for the cross-transfer of buoyancy between the emerged and immersed wedges. In the form GZ = (v * gg1 / V) minus BG * sin(theta), v is the wedge volume, gg1 the horizontal shift between the wedge centroids, V the displaced volume, and BG the vertical separation of B and G. The first term is the buoyancy shift; the second corrects for the height of G above B. It underlies the cross-curves (KN) of stability and the GZ curve used in IMO 2008 IS Code checks. Named after Atwood and Vial (1796).

Source: SNAME Principles of Naval Architecture, Vol. 1 (Stability)