The velocity components of the flow along the moored ship induced by the passing ship are derived from Eq.(2.3). The interaction potential in the unsteady Bernoulli equation gives the pressure distribution and integration of this pressure over the surface gives the net forces on the moored ship.
Assuming zero underwater sectional area at the ends of the moored ship, we get the sway and surge forces as
The yaw moment obtained from the slender body theory, Wang, is
The above equations are for the deepwater case. When the water depth becomes less than twice the draft of the ship, the shallow water effect has to be considered. The bottom condition for an assumed constant water depth of -h is represented by
z = 0. By method of image the interaction forces and moment can be written as
where Sm is the mid-ship section area of the moored ship, Sm' and Sp' are the sectional area slopes of the moored and passing ships, n is the number of images.
The forces and moments are non-dimensionalised as follows
Parabolic Sectional Area Distribution
Sectional area and its slope for both the ships are given by the formula