Journal of Marine Science and Technology

, Volume 15, Issue 2, pp 131–142

Prediction of ship steering capabilities with a fully nonlinear ship motion model. Part 1: Maneuvering in calm water

Original Article

DOI: 10.1007/s00773-010-0084-z

Cite this article as:
Lin, RQ., Hughes, M. & Smith, T. J Mar Sci Technol (2010) 15: 131. doi:10.1007/s00773-010-0084-z

Abstract

This paper introduces a new method for the prediction of ship maneuvering capabilities. The new method is added to a nonlinear six-degrees-of-freedom ship motion model named the digital, self-consistent ship experimental laboratory (DiSSEL). Based on the first principles of physics, when the ship is steered, the additional surge and sway forces and the yaw moment from the deflected rudder are computed. The rudder forces and moments are computed using rudder parameters such as the rudder area and the local flow velocity at the rudder, which includes contributions from the ship velocity and the propeller slipstream. The rudder forces and moments are added to the forces and moments on the hull, which are used to predict the motion of the ship in DiSSEL. The resulting motions of the ship influence the inflow into the rudder and thereby influence the force and moment on the rudder at each time step. The roll moment and resulting heel angle on the ship as it maneuvers are also predicted. Calm water turning circle predictions are presented and correlated with model test data for NSWCCD model 5514, a pre-contract DDG-51 hull form. Good correlations are shown for both the turning circle track and the heel angle of the model during the turn. The prediction for a ship maneuvering in incident waves will be presented in Part 2. DiSSEL can be applied for any arbitrary hull geometry. No empirical parameterization is used, except for the influence of the propeller slipstream on the rudder, which is included using a flow acceleration factor.

Keywords

Ship steering capabilitiesManeuveringSeakeepingRudder angleRudder forceRoll motionComparison of the numerical solution and experimental data

List of symbols

xr,yr,zr

Location of the center of pressure of the rudder

xp

The location of a point, p, on the ship surface

I

Moment vector of inertia about the ship

I(i,i)

Moments of inertia about the ship’s center of mass in the ith direction

F

Force vector acting at the ship’s center of mass in the ship-fixed frame

Γ

Moment vector acting at the ship’s center of mass in the ship-fixed reference frame

Fp, Fq

Exciting force and restoring force acting at the ship’s center of mass in the ship-fixed frame

xc, yc, zc

Center of mass in the ship-fixed coordinate system

x

Unit vector in the ship-fixed coordinate system

xs, ys, zs

Three components of unit vectors in the ship-fixed coordinate

\( \hat{x},\hat{y},\hat{z} \)

Unit vectors in the Earth-fixed coordinate system

X

Translational motion of the ship

Xi

Translational motion of the ship in the i direction

us

Ship speed vector

ur

Effective inflow velocity into the rudder

ut

Total velocity at a point on the ship hull including all ship motions

vs

Translational velocity of the ship’s center of mass

vh

Horizontal component vector of the translational velocity

n

Normal vector of the ship’s surface

nx, ny, nz

Three components of the normal vector of the ship’s surface

β

Drift angle of the ship

δ

Effective rudder deflection angle

ρ

Density of the water in which the rudder is operating

P

Pressure

θ

Rotational angle of the ship

θi

Rotational angle of the ship in the ith direction

Ω

Angular velocity vector of the ship

Ωh

Horizontal angular vector (roll and pitch) of the ship

Ωi

Angular velocity of the ship in the i direction

θ*

Total heading angle, equal to θ3 + β

Ω*

Total heading angular velocity, equal to \( \frac{{\text{d}}\theta^{*}}{{\text{d}}t} \)

η

Free surface elevation

ηe

Environmental free surface elevation

ηs

Free surface deformation due to the ship’s motion

\( \bar{\eta }_{\text{e}} \)

The over bar indicates the average (this is the average of the environmental free surface elevation)

φ

Velocity potential

φe

Velocity potential of the environment, including incident waves

mship

Total ship mass

v

Dissipation coefficient due wave breaking

A0

Surface area of the rudder planform

R3

Moment arm for the rudder force yaw moment

R1

Moment arm for the roll moment

R

Ship maneuvering radius vector

i step

Number of the time step

Fship

Force on the ship’s surface, except on the rudder

Fl

Lift force in the zs coordinate

Frudder

Force on the rudder

Fx

Force on the rudder in the xs direction

Fy

Force on the rudder in the ys direction

Γship

Moment on the ship, except on the rudder

Γrudder

Moment on the rudder

Γrudder(3)

Yaw moment on the rudder

Γc(1)

Roll moment due to the direction of ship speed change

Dtrans

Dissipation of translational motion due to wave breaking [1]

Drotat

Dissipation of rotational motion due to wave breaking and bilge keels

H

Water depth

V

Volume

dV

Element of the volume

xtrack

Track in Earth coordinates

xtrack

Track in the x direction in Earth coordinates

ytrack

Track in the y direction in Earth coordinates

Copyright information

© JASNAOE 2010

Authors and Affiliations

  1. 1.Hydromechanics DepartmentDavid Taylor Model Basin, NSWCCDWest BethesdaUSA