﻿ Line data: Prescribed starting shape

# Line data: Prescribed starting shape

These data are used if the prescribed method is used for step 1 statics. They are found on the prescribed starting shape page of the line data form and can be edited in several ways:

• Editing the length and turn values of a track section on the line data form. OrcaFlex then creates an arc of that length and turn, and the X and Y values at the end of this section (and all subsequent sections) are automatically updated to match.
• Editing the X and Y coordinates of the ends of a track section on the line data form. OrcaFlex creates the uniquely-defined circular arc (or straight line) that is a smooth continuation of the previous section and passes through this new (X,Y) point. The length and turn values for this section (and the X and Y coordinates for all subsequent sections), are automatically updated.
• Dragging the end points of the track sections on a wire frame 3D view using the mouse. This is equivalent to editing its X and Y values.

 Figure: Plan view of example track

The individual data items are as follows.

### End A azimuth

The initial direction of the track.

### Track sections

The number of sections used to define the track.

### Length

The length of the circular arc (or straight line if turn = 0).

### Turn

The amount by which the track azimuth increases over this section. A positive value denotes a turn to the left, when viewed from above, and a negative value denotes a turn to the right. A straight section is represented by a value of 0.

The radius of curvature of the circular arc is calculated from the values of length and turn, and is reported (though not editable). For length $l$ and turn $t$ degrees, the radius is $180\,l / (\pi\, \vert t\vert)$. For straight sections, $t=0$ and the radius is reported as infinity.

 Note: With a non-horizontal seabed, the actual track on the seabed will have a slightly different radius of curvature due to the way the line is laid out, as discussed below.

### X and Y

The global $X$ and $Y$ coordinates of the end of this track section. You can edit these values directly, on the line data form, or you can adjust them by dragging the end point on a wire frame 3D view. If you change X or Y (by either method), then OrcaFlex fits a circular arc (starting at the previous section's end point) through the new end point and updates the length and turn values automatically to match this new arc.

### Z, arc length, azimuth

Respectively, these are the global $Z$-coordinate of the section end point on the seabed, the cumulative arc length to the end of the section, and the azimuth direction at the end of the section. These values are all derived from the other data: they are reported for information, and are not editable.

### Drawing

The data which control the drawing, or not, of the spline and the pen used, are on the line drawing page.

## Laying out the line

The track data defines a sequence of straight lines and circular arcs in the horizontal plane, which are then projected vertically onto the seabed to define the track itself. OrcaFlex then lays the line out along the track, allowing for any as laid tension specified on the line data form.

Because the line is modelled as a series of straight segments, when the line is laid out along a curved track it will repeatedly 'cut corners' and so the length of line laid along a given curved track section will be slightly shorter than the length of that section. The size of this discrepancy reduces as more segments are used.

If end A is above the seabed then the height above the seabed varies linearly between end A and the first track section point, reaching the seabed at the end of the first track section. If the end of the last track section is reached before all the line has been laid out, then the rest of the line is laid out in a straight line in the direction of the end of the track.

### Sloping and profiled seabeds

The track on the seabed is obtained by projecting the specified circular arcs or straight sections vertically down onto the seabed. With a horizontal seabed this vertical projection has no effect on the shape of the track. But, if the seabed is not horizontal, the vertical projection does not preserve distances and this causes some effects that users should note:

• The section lengths and arc lengths that appear in the prescribed starting shape data table are lengths in the horizontal plane, i.e. before projection down onto the seabed. On a non-horizontal seabed the true section and arc lengths on the seabed will differ, the difference depending on the slope of the seabed. The actual arc lengths can be obtained by running the static analysis and looking at the summary results for the line.
• The section radius reported in the prescribed starting shape data table is that of the circular arc in the horizontal plane, i.e. before projection down onto the seabed. When the circular arc is projected down onto a non-horizontal seabed the resulting track section is no longer circular, so again the actual radius of curvature will differ. The actual radii of curvature can be obtained by running the static analysis and looking at the summary results for the line.