Only using the first order hydrodynamic pressure on the panel element to estimate the hydrodynamic force acting on the submerged panel element may miss the equivalent gravity force component. In the output file .ahf, the equivalent gravity force on the panel element is included.

It is assumed that both the amplitude of the incident wave and the amplitude of the corresponding structural motion responses are small. Under this assumption, the perturbation approach is employed to express the fluid properties and the positions of the points on structure:

(1–1)

Denoting as the normal vector of the structure surface at the point when the structure is at its mean position in still water, the first order component of the normal vector is written as:

(1–2)

where is the first order variation of the normal vector of a body surface location in the fixed reference axes (FRA), , of which is the first order rotational motion vector.

The fluid pressure at a given point is determined by the Bernoulli's equation and can be represented as a Taylor series:

(1–3)

where

(1–4)

In the fixed reference axes, the total force (up to the first order) acting on the centroid of a submerged panel is:

(1–5)

In the equation above, the zero-order force (the hydrostatic force) is:

(1–6)

The first order hydrodynamic force is:

(1–7)

The second term at the right-hand side of Equation 1–7 is referred to as the first order hydrodynamic pressure induced force, which consists of the first order incident/diffraction/radiation wave force and the hydrostatic varying force, due to the change of the vertical position of the panel centroid. The first term is a new component, which is the hydrostatic varying force due to the change of the panel normal vector.