## Line results: Angles |

Node azimuth, node declination, node gamma

Azimuth, declination and gamma are available at mid-segment points and line ends. Node azimuth, node declination and node gamma are available at nodes.

These angles report the local orientation of the line relative to global axes. The gamma angle is defined as for line ends.

Declination is in the range 0° to 180°. Range jump suppression is applied to azimuth and gamma, so it is possible for values outside the range -360° to +360° to be reported.

Available at nodes, these angles define the orientation of the node relative to its static orientation. Considered as the components of a vector, $\vec{R} = (Rx, Ry, Rz)$, they define the rotation from the static orientation to the instantaneous orientation. The rotation is about the direction of $\vec{R}$ and has magnitude $|\vec{R}|$.

Available at mid-segment points and line ends. The direction angles of the results point (either an end node or a mid-segment point), relative to the end axes of the nearest line end.

Ez angle is in the range 0° to 180°. Range jump suppression is applied to Exy angle, Ezx angle and Ezy angle, so values outside the range -360° to +360° might be reported.

Available at mid-segment points. The twist per unit length experienced by the segment.

Available at nodes. The angle between the direction of the principal fluid relative velocity and the line axial direction, in the range 0° to 90°.

Available at line ends. The azimuth and declination angles, relative to global axes, of the no-moment direction $E_\mathrm{z}$ at the end, allowing for any motion of the object to which the line is connected. These results are only available if the end orientation angles are defined.

The no-moment declination is in the range 0° to 180°. Range jump suppression is applied to no-moment azimuth, so values outside the range -360° to +360° might be reported.

Available at line ends. The azimuth and declination of the end force vector, relative to global axes.

End force declination is in the range 0° to 180°. Range jump suppression is applied to end force azimuth, so values outside the range -360° to +360° might be reported.

Available at line ends. The direction angles of the end force vector, with respect to the frame of reference of the line end. These results are only available if the end orientation angles are defined.

End force Ez angle is in the range 0° to 180°. Range jump suppression is applied to the other 3 end force angles, so values outside the range -360° to +360° might be reported.

Available only at nodes that use one of the vortex tracking VIV models. The values reported are the angular positions of the stagnation and separation points.