OrcaFlex Manual - Orcina

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System Modelling: Data and Results, Lines
single representative line type. Single representative values for mass, diameters, stiffnesses, etc. must be calculated
and the equivalent line type category is designed to perform those calculations.
The input data for an equivalent line type comprises the following:
1. A carrier line type. This is a reference to an existing line type defined in the model.
2. One or more secondary lines. These secondary lines are also defined by referencing existing line types.
Secondary lines can be either internal or external.
3. Other data. Not all equivalent line data can be derived by the program, e.g. drag, lift, added mass, fluid inertia,
etc. Such data is provided by the user.
Carrier Line
The equivalent line properties are made by combining properties from a number of other line types. One of these
line types is decreed to be the carrier line and is treated differently from the other secondary lines in the following
ways:
� Any internal secondary lines are deemed to be inside the bore of the carrier line.
� The carrier line, together with the internal secondary lines, determines the cross-sectional area associated with
the line contents data specified on the Line data form.
� Stress results are reported for the carrier line.
Secondary Lines
Secondary lines are used to specify lines either internal or external to the carrier line. Multiple secondary lines can
be defined. For each secondary line, the contents density must also be specified. This contents density is associated
with the bore of the secondary line. The axial, bending and torsional stiffnesses of each secondary line can be
specified as contributing or not contributing to the equivalent line's stiffness.
Other Data
Drag/lift coefficients, drag/lift diameters, added mass/inertia coefficients, CG Offset and Allowable Tension are all
specified explicitly for an equivalent line.
Modelling Details
The program derives equivalent values for the line type as described in the subsequent sections. The values can be
viewed using the All view mode, or alternatively from the Line Type properties report.
In order to express the equivalent line property derivations we need to establish notation that distinguishes
between the various different line types involved. We will use subscript notation as follows:
Geometry
e indicates properties of the equivalent line, e.g. ODe
c indicates properties of the carrier line, e.g. ODc
int[i] indicates properties of the ith internal secondary line, e.g. ODint[i]
ext[i] indicates properties of the ith external secondary line, e.g. ODext[i]
ODe is calculated to give a displacement equal to the displacement of the carrier line together with all the external
lines:
ODe = √(ODc 2 + Σ ODext[i] 2 )
IDe is calculated to give an internal cross-sectional area equal to that of the carrier line minus the external crosssectional
area of all the internal lines:
Mass
IDe = √(IDc 2 - Σ ODint[i] 2 )
Mass per unit length, Me, is the sum of the mass per unit length for the carrier line and all secondary lines:
Structure
Me = Mc + Σ Mint[i] + Σ Mext[i]
Axial stiffness, EAe, is the sum of the EA for the carrier line and all secondary lines that contribute to axial stiffness: