OrcaFlex Manual - Orcina

Theory, Line Theory
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The velocity vectors used in the calculation are the translational velocity, V, and angular velocity, Ω, of the wavefrequency
part of the vessel primary motion velocity relative to the earth, at the reference origin. The damping load
is then applied at that reference origin.
The damping model used depends on the vessel type symmetry, as follows.
If the symmetry is not Circular then the damping model treats each degree of freedom independently, and the
damping force, F, and moment, M, are given by:
where
Fx = - Lsurge Vx - Qsurge Vx |Vx|
Fy = - Lsway Vy - Qsway Vy |Vy|
Fz = - Lheave Vz - Qheave Vz |Vz|
Mx = - Lroll Ωx - Qroll Ωx |Ωx|
My = - Lpitch Ωy - Qpitch Ωy |Ωy|
Mz = - Lyaw Ωz - Qyaw Ωz |Ωz|
L and Q are the linear and quadratic other damping coefficients, respectively
subscripts x, y, z denote the vessel primary heading directions (so x & y are horizontal and z vertical).
If the vessel type symmetry is Circular, then the quadratic term instead uses a cross-flow drag model, with a
vertical axis:
where
Fx = - Lsurge Vx - Qsurge Vx |Vh|
Fy = - Lsway Vy - Qsway Vy |Vh|
Fz = - Lheave Vz - Qheave Vz |Vz|
Mx = - Lroll Ωx - Qroll Ωx |Ωh|
My = - Lpitch Ωy - Qpitch Ωy |Ωh|
Mz = - Lyaw Ωz - Qyaw Ωz |Ωz|
Vh = (Vx, Vy, 0) = horizontal vector component of V
Ωh = (Ωx, Ωy, 0) = horizontal vector component of Ω.
5.12 LINE THEORY
5.12.1 Overview
OrcaFlex uses a finite element model for a line as shown in the figure below.