Journal of Marine Science and Technology

, Volume 19, Issue 4, pp 376–393

# Directional stability of a ship in close proximity to channel wall

Original article

## Abstract

Ship maneuvering motions are affected by so-called bank suction forces when proceeding in close proximity to channel wall. In fact, some rudder angles would be required to maintain the course and proper rudder activities are needed to be directionally stable. The authors conducted captive model tests in a channel with variations in water depth, off-centerline displacement, ship speed, hull drift angle and rudder angle. The shallow water and bank effects on the hydrodynamic force characteristics were investigated. Based on the regression mathematical model, the rudder angle and hull drift angle required at equilibrium conditions were estimated and the limiting off-centerline displacement for safe operation was proposed. Directional stability in the channel was also studied based on the eigenvalue analysis and dynamic maneuvering motion simulations. The stable/unstable zone for course keeping according to control system characteristics would be important for the maneuvering operation.

### Keywords

Directional stability Equilibrium condition Bank effect Shallow water effect

### List of symbols

$$m$$

Ship mass (kg)

$$I_{\rm z}$$

Yaw moment of inertia (kg m$$^2$$)

$$m_{11}$$

$$m_{22}$$

$$m_{26}$$

Added mass coupled between sway and yaw (kg m)

$$m_{66}$$

Added moment of inertia in yaw (kg m$$^2$$)

$$g$$

Gravity acceleration (ms$$^{-2}$$)

$$L$$

Ship length between perpendiculars (m)

$$B$$

$$d$$

Ship draft (m)

$$x_{\rm G}$$

Longitudinal position of the center of gravity of ship (m)

$$\rho$$

Water density (kg m$$^{-3}$$)

$$U$$

Ship speed (ms$$^{-1})$$

$$F_{\rm n}$$

Froude number $$(U/\sqrt{gL})$$

$$u$$

Surge velocity (ms$$^{-1}$$)

$$v$$

Sway velocity (ms$$^{-1}$$)

$$r$$

yaw rate (s$$^{-1}$$)

$$\psi$$

$$\beta$$

Hull drift angle

$$\delta$$

Rudder angle

$$\eta$$

Off-centerline displacement (m)

$$Y$$

Sway force (N)

$$N$$

Yaw moment around midship (Nm)

$$G_1$$

Proportional gain constant for rudder control

$$G_2$$

Differential gain constant for rudder control (s)

$$h$$

Water depth (m)

$$W$$

Channel width (m)

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