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Steady sailing performance of a ship in the proximity to the bank under windy conditions

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Abstract

This paper presents a method to efficiently calculate steady sailing conditions such as check helm, speed drop, hull drift angle, etc. of a ship moving in parallel to a bank wall under steady wind, together with the course stability at the equilibrium condition. Using this method, this study investigates the bank effect on the steady sailing condition and the course stability of a pure car carrier in steady wind and it evaluates the limiting wind condition for safe navigation (maneuvering limit). In case of head wind, a significant speed drop appears. In case of oblique head wind from the port side, the hull drift angle increases significantly and there is a distinct possibility that the ship touches the bank wall. In case of oblique following wind from the port side, the check helm increases significantly, because the wind force is added to the bank suction force. This becomes critical when the ship moves closer to the bank and in more shallow water areas, and the maneuvering limit level becomes more severe. The present method is a useful tool for measuring the maneuvering limit of a ship moving in close proximity to the bank under steady wind.

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Abbreviations

CS:

Course stability

MCR:

Maximum continuous rating (of main engine)

MMG:

Maneuvering modeling group

NOR:

Normal rating

PCC:

Pure car carrier

SSC:

Steady sailing condition

\(\alpha _z\) :

Vertical acting point of the lateral added mass component \(m_y\)

\(\beta\) :

Hull drift angle at midship

\(\overline{{\gamma }_R}\) :

Averaged flow straightening coefficient

\(\delta\) :

Rudder angle

\(\eta\) :

Lateral deviation of the ship centerline at midship position from \(x_0\)-axis

\(\theta _A\) :

Relative wind direction

\(\theta _W\) :

Absolute wind direction

\(\rho\) :

Water density

\(\rho _a\) :

Air density

\(\phi\) :

Roll angle

\(\psi\) :

Ship heading

\(\nabla\) :

Displacement volume of the ship

\(A_X\), \(A_Y\) :

Front and side profile areas of the ship in air, respectively

\(A_R\) :

Rudder profile area

\(a_H\) :

Rudder force increase factor

B :

Ship breadth

\(C_b\) :

Block coefficient

\(C_{XA}\), \(C_{YA}\), \(C_{NA}\), \(C_{KA}\) :

Aerodynamic force coefficients with respect to surge force, lateral force, yaw moment and roll moment, respectively

\(D_P\) :

Propeller diameter

d :

Ship draft

\(F_N\) :

Rudder normal force

\(\overline{GM}\) :

Metacentric height

\(G_1, G_2\) :

Control gains for autopilot

g :

Gravity acceleration

\(H_R\) :

Rudder span length

h :

Water depth

\(I_{xx}, I_{zz}\) :

Moment of inertia of the ship around \(x-\) and \(z-\)axes, respectively

\(J_{xx}, J_{zz}\) :

Added moment of inertia around \(x-\) and \(z-\)axes, respectively

\(\overline{KM}\) :

Metacenter height above baseline

\(K_{\dot{\phi }}\), \(K_{\dot{\phi }\dot{\phi }}\) :

Roll damping coefficients

\(k_{xx}\) :

Radius of roll gyration including added moment of inertia with respect to the roll

L :

Ship length between perpendiculars

m :

Ship’s mass

\(m_x\), \(m_y\) :

Added masses of the x-axis direction and y-axis direction, respectively

\(N_{MCR}\) :

Propeller revolution at MCR

\(N_P\) :

Propeller revolution

\(N_S\) :

Propeller revolution at \(P_S\)

\(N_v'\), \(N_r'\), \(N_{\phi }'\), \(N_{vvv}'\), etc.:

Hydrodynamic derivatives with respect to yaw moment

\(o-xyz\) :

Horizontal body-fixed coordinate system considering the origin at midship

\(o_0-x_0y_0z_0\) :

Space-fixed coordinate system

\(P_{MCR}\) :

Engine power at MCR

\(P_S\) :

Engine power at NOR with \(15\%\) sea margin

\(Q_{EMAX}\) :

Maximum propeller torque of the main engines

\(R_0\) :

Ship resistance in straight moving

r :

Yaw rate

s :

Distance from the bank toe to ship side

T :

Propeller thrust

t :

Time

\(t_P\) :

Thrust deduction factor

\(t_R\) :

Steering resistance deduction factor

U :

Resultant speed (\(=\sqrt{u^2+v_m^2}\))

\(U_W\) :

Absolute wind velocity

u, v :

Surge velocity and lateral velocity at the center of gravity,

respectively

\(V_A\) :

Relative wind velocity

\(V_S\) :

Design speed of the ship

\(v_m\) :

Lateral velocity at midship

W :

Distance from the bank toe at the sea bottom to ship center line

X, Y, N, K :

Surge force, lateral force, yaw moment, and roll moment with the exception of added mass components, respectively

\(X_A\), \(Y_A\), \(N_A\), \(K_A\) :

Surge force, lateral force, yaw moment, and roll moment due to wind

\(X_H\), \(Y_H\), \(N_H\) :

Surge force, lateral force, and yaw moment acting on the ship hull with the exception of added mass components, respectively

\(X_P\) :

Surge force due to the propeller

\(X_R\), \(Y_R\), \(N_R\) :

Surge force, lateral force, and yaw moment by steering, respectively

\(X_{vv}'\), \(X_{rr}'\), \(X_{\phi \phi }'\), \(X_{vr}'\) etc.:

Hydrodynamic derivatives with respect to surge force

\(x_G\) :

Longitudinal coordinate of the center of gravity of the ship

\(x_H\) :

Longitudinal coordinate of the acting point of the additional lateral force component induced by steering

\(x_R\) :

Longitudinal coordinate of the rudder position (\(=-0.5L\))

\(Y_{H0}\) :

Hull lateral force excluding bank effect

\(Y_{H\eta }\) :

Hull lateral force components including bank effect

\(Y_v'\), \(Y_r'\), \(Y_{\phi }'\), \(Y_{vvv}'\) etc.:

Hydrodynamic derivatives with respect to lateral force

\(z_G\) :

Vertical coordinate of the center of gravity of the ship

\(z_H\) :

Vertical coordinate of the acting point of the hull lateral force

\(z_{H0}\) :

Vertical coordinate of the acting point of hull lateral force components excluding bank effect

\(z_{H\eta }\) :

Vertical coordinate of the acting point of hull lateral force components including bank effect

\(z_R\) :

Vertical coordinate of the acting point of the rudder force

subscript 0:

Implies a steady term

substituting \({\varDelta }\) :

Implies an unsteady term

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Acknowledgements

This study was supported by the JSPS KAKENHI Grant Number JP26249135. The author expresses his sincere gratitude to Mr. R. Sakuno for his assistance with the captive model tests in shallow water.

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Authors and Affiliations

  1. Department of Transportation and Environmental Systems, Hiroshima University, Kagamiyama 1-4-1, Higashi-Hiroshima, Hiroshima, 739-8527, Japan

    Hironori Yasukawa

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  1. Hironori Yasukawa
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Correspondence to Hironori Yasukawa.

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Yasukawa, H. Steady sailing performance of a ship in the proximity to the bank under windy conditions. J Mar Sci Technol 25, 1246–1265 (2020). https://doi.org/10.1007/s00773-020-00712-x

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