# Direction conventions

Directions and headings are defined in the horizontal plane in OrcaFlex as the azimuth angle of the direction, in degrees, measured positive from the $x$-axis towards the $y$-axis, as shown in the following figure.

Directions for waves, current and wind are specified by giving the direction in which the wave (or current or wind) is progressing, relative to global axes. In other words for these directions the $x$- and $y$-axes in the above figure correspond to global $G_\mathrm{X}$ and $G_\mathrm{Y}$ axes.

Vessel headings are specified as the direction in which the vessel $V_\mathrm{x}$-axis is pointing, relative to global axes. So again, for vessel headings the $x$- and $y$-axes in the above figure correspond to the global $G_\mathrm{X}$ and $G_\mathrm{Y}$ axes.

Vessel responses to waves depend on the wave direction relative to the vessel, and similarly for current and wind. For example, vessel type RAOs and QTFs are given for a specified wave direction relative to vessel axes $(\beta = \text{wave direction relative to global axes} - \text{vessel heading})$. In other words, for these vessel-relative directions the $x$-axis in the above figure is in the vessel heading direction. Hence a relative wave direction of $\beta=\text{0°}$ means a wave coming from astern and a relative direction of $\beta=\text{90°}$ means one coming from starboard.

The slope direction for the seabed is defined as the direction that points up the steepest slope, relative to global axes.

The slope direction of a plane shape that is fixed or anchored is specified relative to global axes.

The slope direction of a plane shape that is connected to another object is specified relative to that object's axes.

### Azimuth and declination

Directions are defined in 3D in OrcaFlex by giving two angles, azimuth and declination, that are broadly similar to those used in navigation, gunnery, etc. As in the horizontal case, directions are sometimes defined relative to the global axes and sometimes relative to the local object axes.

For directions defined relative to the object local axes $L_\mathrm{xyz}$, the azimuth and declination angles are defined as follows:

• Azimuth is the angle from the $x$-axis to the projection of the direction onto the $xy$ plane. The positive $x$-axis direction therefore has azimuth = 0°, and the positive $y$-axis direction has azimuth = 90°.
• Declination is the angle the direction makes with the $z$-axis, so is therefore 0° for the positive $z$-direction, 90° for any direction in the $xy$ plane, and 180° for the negative $z$-direction. When declination is 0° or 180°, azimuth is undefined (OrcaFlex reports azimuth = 0° in these cases).

Directions relative to the global axes are defined in just the same way, simply replacing the local $xyz$ directions above with the global $XYZ$ directions. A global declination of 0° therefore means vertically upwards, 90° means horizontal and 180° means vertically downwards.

When a direction is being defined, the sign of the direction must also be defined. For example, "vertical" does not fully define a direction – it must be either "vertically up" or "vertically down" before the azimuth and declination angles can be determined. The direction sign conventions used in OrcaFlex are

• for lines and links, axial directions are always defined from end A towards end B. Thus a vertical line or link with end A at the top has declination 180°.
• for winches, axial directions are defined from the last connection point towards the next-to-last connection point. So, for example, a winch with two connections, the second directly above the first, has declination 180°.