# Influence of Water Depth on Ship Maneuvering Behavior

## Background and Objectives

Most ship maneuvers take place in restricted waters e.g. in harbors. The investigation of the ship maneuvering behavior is normally performed in deep water towing tanks. Previous investigations show that the water depth has a significant influence on the maneuvering behavior of ships.

## Computational Approach

Numerical computations are conducted to investigate the influence of water depth. For the computations FreSCo+, a in-house developed CFD-code based on the RANS equations, is applied.

In the numerical study the captive motions of a ship hull according to the Planar Motion Mechanism used in model testing are simulated. The aim of the numerical calculation is the calculation of the hydrodynamic coefficients for a nonlinear maneuvering model. The results of the computations are the time dependent forces on the model. Subsequent Fourier analysis and regressions with the method of least square lead to the hydrodynamic coefficients of the ship hull. The calculations are done on deep and on shallow water for a series 60 ship C_{B}=0.7. The influence of the propeller on the flow is simulated by a body force model. The trim and sinkage as well as deformation of the free surface are not considered.

For validation of the deep water case, model tests performed by Wolff (1981) are used. The results for transverse force and yaw moment show a good agreement (Figure 1, green: calculated force; red: measured force by Wolff). The longitudinal force shows some discrepancies at low axial velocities (Figure 2), further investigation is needed.

With the calculated hydrodynamic coefficients several maneuvers are used to estimate the external forces acting on the ship. Integration of the ship acceleration with the Runge-Kutta scheme delivers the velocities. By integrating these velocities the track and the motion of the ship can be calculated.

The turning circle maneuver is simulated at three different ruder angles in deep water and in shallow water (ratio of water depth to ship draft=1.2). The results in figure 3 show the strong effect of the water depth on the turning circle radius.

## Cooperation partner

Prof. Dr.-Ing Andres´ Cura-Hochbaum, Technische Universität Berlin