The vertical motions of a vessel (pitch and heave) are most readily calculated by subdividing the vessel into a number of transverse strips and considering the forces on each of the strips. The two dimensional added mass, damping and restoring coefficients are calculated for each strip, and the respective global coefficients are then found by integrating along the length of the hull. It is assumed that the amplitude of oscillation is sufficiently small that the response of the vessel will remain linearly proportional to the amplitude of the waves.

The global added mass and damping are calculated according to the method developed by Salvesen et al. (1970). Two formulations are used: the first ignores the transom terms; whilst these terms are included in the second.

The coefficients in the equations of motion are summarised below, these are the same for both the transom terms and no transom terms versions:

For the transom terms version, the following terms are added to the coefficients given above:

where the variables are defined as follows:

The integrals are all over the length of the hull.