﻿ Line results: Analytic catenary

# Line results: Analytic catenary

For lines that use the analytic catenary representation, only a subset of the usual line results are available, as well as a few special results that are unique to analytic catenary lines.

Unlike lines that use the finite element representation, lines that use the analytic catenary representation are not discretised into nodes and segments during the calculation. However, these notions of nodes and segments are still useful when defining results and – in this context only – the data on the line structure page has relevance for analytic catenary lines. In particular, requesting a result at a given node will return values at the arc length at which that node is defined. However, unlike in the finite element representation, the analytic catenary results for a line are defined at all arc lengths, not just those pertaining to a particular node or segment. It is therefore possible to interrogate the line for its results along a continuum of arc lengths.

## Positions

### X, Y and Z

The global coordinates of the point on the line at the selected arc length.

### Layback

The horizontal component of distance between the point on the line at the selected arc length and the touchdown point.

### Arc length

The arc length from end A to the selected point. This is generally only useful for the touchdown point, since for other points it is constant. For the touchdown point it gives the arc length from end A to the first point on the seabed, or zero if there is no touchdown.

The vertical displacement of the fairlead from its position in reset state. This quantity is defined analogously to the fairlead vertical offset steps that are used to specify the analytic catenary solution grid and can provide a useful cross-check of the solutions.

## Angles

### Declination

The angle that the axis of the line makes to the vertical at the given arc length, reported in degrees.

## Forces

### Effective tension

The tension in the line at the given arc length.

### Horizontal tension at first suspended point

The horizontal component of the tension at the nearest point to the bottom end of the line that does not lie on the seabed. This quantity is defined analogously to the horizontal tension steps that are used to specify the analytic catenary solution grid and can provide a useful cross-check of the solutions.

### Vertical component of tension

The vertical component of tension at the given arc length.

### Horizontal component of tension

The horizontal component of tension at the given arc length.

### End force,End GX force, end GY force and end GZ force,End Lx force, end Ly force and end Lz force,End Ex force, end Ey force and end Ez force

These results report the magnitude of the end force and its components in the following directions:

• The directions of the global axes $\GXYZ$.
• The directions of the local axes $\Lxyz$ of the parent object to which the line end is connected. For example, if the line end is connected to a vessel, the $\Lxyz$ axes are the directions of the vessel axes.
• The directions of the line end axes $\Exyz$.