# Vessel theory: Frames of reference

Vessels make use of a greater number of frames of reference than any other OrcaFlex object. The loads available for application to an OrcaFlex vessel are defined by several different modelling approaches. In order to correctly combine vessel loads, new frames of reference are required in addition to the typical instantaneous frame. However, we begin by considering the familiar instantaneous frame below.

## Vessel frame of reference

The vessel frame is defined relative to a right-handed system of local vessel axes $\Vxyz$ illustrated below, where:

• $V$ is the vessel origin for this vessel type. This is effectively chosen when the vessel type is set up. The origin is never defined explicitly: it is simply the point on the vessel to which all the vessel type data (or their reference origins) refer. It is entirely arbitrary and may, for instance, be at the bow on the keel, at the centre of mass, etc. However note that if you specify that the vessel type has symmetry then the vessel origin must be placed on the plane(s) of symmetry or at the centre of circular symmetry.
• $V\urm{x}$, $V\urm{y}$, and $V\urm{z}$ are the axes of surge, sway and heave, respectively, for this vessel type. Diffraction analysis RAO data used in OrcaFlex must therefore define surge, for instance, to be positive or negative along the $V\urm{x}$ axis.

 Figure: Vessel model

Points on the vessel, for example where cables or risers are connected, are then defined relative to these vessel axes. These points then move with those axes as the vessel moves and rotates relative to the global axes, and OrcaFlex calculates these motions automatically.

## Primary frame

The primary frame is an instantaneous frame whose motion is defined using only vessel primary motion. Superimposed motion is applied using the motion of the primary frame as a starting point, as its name would suggest.

## Diffraction frame

Vessel data obtained from diffraction analysis must be applied, in OrcaFlex, in a frame of reference that best represents the original diffraction model. Specifically, diffraction analysis involves solving the potential theory problem for a vessel hull whose position is defined relative to the still water surface. This is represented in OrcaFlex by the reference origin datum position for vessel type stiffness, added mass and damping. Displacement of this reference origin relative to its datum position generates a buoyancy (stiffness) load on the vessel, the size of which is determined by the hydrostatic stiffness matrix; the changing buoyancy loads due to applied waves are, on the other hand, accounted for within the load RAO data.

OrcaFlex therefore defines the diffraction frame as having a constant rotational offset from the primary frame, whereby the diffraction frame $z$-axis is perpendicular to the still water surface when the vessel primary frame is in the datum orientation. So the constant rotation between these two frames corresponds to the vessel datum heel and trim. When vessel datum heel and trim angles are both zero, the diffraction frame and primary frames coincide.

At times a vessel frame of reference is required which is aligned to the still water surface - i.e. a frame with horizontal $x$-$y$ plane. Such frames can still change heading, rotating about the global vertical axis, so in OrcaFlex we name them heading frames.

## Filtered frames

In order to combine different vessel loads or motions with proper consideration of the models underlying the corresponding different data sources involved, OrcaFlex filters the vessel primary motion.

The primary low frequency frame has motion defined by the low frequency part of the filtered primary motion. It is affected by the choices made under the primary motion is treated as data item.

Yet another frame, the primary low frequency heading frame is also required at this point. This frame has translation and yaw rotation defined by the low frequency part of the filtered primary motion, but roll and pitch rotations are suppressed. The $z$-axis of the primary low frequency heading frame is thus always vertically upwards.

## Load frame of reference

When a load is applied to a vessel, some frame of reference must be chosen for that load. A good example is buoyancy force, which can be expressed most simply as a single-component vector using any frame that has one axis aligned with the global vertical direction. Changing the frame of reference used to interpret a load can introduce nonlinear effects into a time domain simulation, or additional linear dynamic contributions from mean loads in the frequency domain.

The loads obtained from diffraction analysis are also sensitive to the frequency of any motions made by their interpreting frame, because the original potential theory solution is separated into parts using frequency content information. Therefore, OrcaFlex must then take the same care when applying these diffraction effects in our further analysis.

Because the effect of choosing a frame of reference can be significant, vessels offer users a choice in the calculation mode data item, labelled using the most important consequences for time domain analysis.

• If calculation mode is set to filtering, then diffraction loads are applied using heading frames, and filtered heading frames are used when appropriate.
• If calculation mode is set to QTF modification, then diffraction loads are generally applied using unfiltered frames which may rotate away from horizontal. A heading frame is still used for hydrostatic stiffness.