# Vessel data: Calculation data

The calculation data give you overall control of the ways in which the vessel's static position and dynamic motion are determined. You may find vessel modelling overview helpful in identifying the data relevant to the situation you wish to model.

## Included in static analysis

For a vessel whose connection is free, you can control whether the static analysis calculates the static equilibrium position of the vessel, or simply leaves the vessel in its user-specified initial position. Included in static analysis specifies the vessel degrees of freedom, if any, to be included in this calculation. The choices available are:

• None. The vessel simply remains in its initial position. You should be aware that this is not necessarily an equilibrium position.
• 3 DOF. OrcaFlex starts from the initial position and adjusts the vessel's X, Y and heading to an equilibrium position. Note that these three are the only free degrees of freedom of the vessel in the calculation. The remaining three (Z, heel and trim) remain at their initial values, as if the vessel were physically constrained in these directions. Consequently, the $Z$-component of resultant force, and the resultant heel and trim moments, may be non-zero in the equilibrium position.
• 6 DOF. OrcaFlex finds an equilibrium position for all six degrees of freedom. In this case, all of the X, Y, Z forces and heel, trim, heading moments will be zero at the equilibrium position.

The loads on the vessel to be taken into account are governed by the included effects. In the static analysis there are no waves, so many of these loads (first order wave load, sum frequency QTF, added mass and damping, manoeuvring and other damping) will be zero, and wave drift load will only include the mean drift load (allowing for wave drift damping, if included), not any slowly varying contribution.

## Time domain dynamic analysis

When conducting time domain analysis OrcaFlex provides two forms of vessel motion, primary and superimposed, for a vessel whose connection is free. When both are applied, this is done concurrently with the latter being (as the names suggest) superimposed on the former. The vessel modelling overview contains some examples of the way in which these different forms of motion can be used.

### Primary motion

The primary motion determines what we refer to, in OrcaFlex, as the primary position of the vessel. The primary motion takes one of the following forms:

• None. No primary motion: the primary position of the vessel remains fixed at the position determined by the static analysis.
• Prescribed motion allows you to drive the vessel around the sea surface, for example to model the vessel moving station during the simulation. The vessel's speed and course are defined by the prescribed motion data on the primary motion page.
• Calculated (3 DOF). OrcaFlex calculates the vessel primary motion in only three degrees of freedom (surge, sway, yaw) based on the included effects plus loads from any child objects connected to the vessel. There is no primary motion in heave, roll, or pitch. The data for each of the the included effects must be defined.
• Calculated (6 DOF). Here, OrcaFlex calculates the vessel motion in all six degrees of freedom, based on the included effects, plus loads from any lines or other child objects that are connected to the vessel. The stiffness and reference origin datum position of the vessel type must be specified, plus the data for all the included effects.
• Time history. The primary motion is given by a time history that defines, as a function of time, the vessel primary X, Y, Z, rotation 1, rotation 2 and rotation 3. The time history data are defined on the primary motion page.
• Externally calculated. The primary motion is defined by an external function, specified on the primary motion page.

### Superimposed motion

The superimposed motion is applied as an offset from the position given by the primary motion. It takes one of the following forms:

• None. There is no offset and the vessel is at the primary position at all times.
• RAOs + harmonics. The vessel position oscillates harmonically about the primary position. The harmonically-varying offset may have contributions from two sources: firstly, in the presence of waves and with non-zero displacement RAOs, wave-generated harmonic motions specified by those RAOs; and secondly, any harmonic motions defined on the superimposed motion page of the vessel data form.
• Time history. The offset is defined by a time history which gives the vessel surge, sway, heave, roll, pitch and yaw as a function of time. The time history data are defined on the superimposed motion page.

## Frequency domain dynamic analysis

For a frequency domain analysis, the data required depend on the solution frequencies being solved for. For a low frequency solve you will need to define the form of the low frequency motion; correspondingly, for a wave frequency solve you will need to define the form of the wave frequency motion; and a low frequency solve with combined linearisation will require both. These two forms then define the motion of the vessel about the position determined by the static analysis.

### Low frequency motion

Vessel low frequency motion takes one of the following forms:

• None. There is no low frequency motion about the position determined by the static analysis.
• Calculated (3 DOF). OrcaFlex calculates the vessel low frequency motion, about the static position, in only 3 degrees of freedom (surge, sway, yaw) based on any low frequency included effects, plus loads from any lines or other child objects connected to the vessel. There is no low frequency motion in the other 3 degrees of freedom (heave, roll, pitch). The data for all the relevant included effects must be defined.
• Calculated (6 DOF). Vessel low frequency motion, about the static position, is calculated in all six degrees of freedom, based on the low frequency included effects, plus loads from any lines or other child objects connected to the vessel. The stiffness and reference origin datum position of the vessel type must be defined, together with the data for all the relevant included effects.

### Wave frequency motion

Vessel wave frequency motion has the following possible forms:

• None. There is no wave frequency motion about the position determined by the static analysis.
• Displacement RAOs. The vessel will oscillate harmonically, about the static position, as determined by the vessel type displacement RAOs and the wave elevation process.
• Calculated (3 DOF). OrcaFlex calculates the vessel wave frequency motion, about the static position, in only 3 degrees of freedom (surge, sway, yaw) based on the wave frequency included effects, plus loads from any lines or other child objects that are connected to the vessel. There is no wave frequency motion in the other 3 degrees of freedom (heave, roll, pitch). The data for all the relevant included effects must be specified.
• Calculated (6 DOF). Here OrcaFlex calculates the vessel wave frequency motion, about the static position, in all 6 degrees of freedom, based on the wave frequency included effects, plus loads from any lines or other child objects connected to the vessel. The stiffness and reference origin datum position of the vessel type must be defined, together with the data for all the relevant included effects.

## Included effects

For all types of analysis, each of the following vessel load effects can be included in the analysis by ticking its corresponding check box on the calculation page of the vessel data form:

 Notes: Included effects will only influence the vessel static equilibrium position if included in static analysis is other than none. In the time domain included effects will only influence the vessel motion if the primary motion is one of the calculated forms. In the frequency domain included effects will only affect the vessel motion if the wave frequency or low frequency motion takes one of the calculated forms. In addition, the different load effects are associated with low frequencies, wave frequencies, or in some cases both. When a load effect is, for instance, associated with wave frequencies only, it is not applied in a low frequency solve even if the corresponding included effect check box is ticked. Likewise, when a load effect is associated with low frequencies only, it is not applied in a wave frequency solve even if the corresponding included effect check box is ticked.

## Primary motion is treated as, dividing period

In time domain analysis, some of the included effects depend on only the low frequency primary motion, some depend on only the wave frequency primary motion, and some depend on all the primary motion. For details see vessel modelling overview. Consequently, if a vessel has any primary motion, you must choose whether the primary motion is treated as all low frequency, all wave frequency, or a mixture of both low and wave frequency.

If you choose it to be a mixture of both, you must also define a dividing period that is used to filter the primary motion into its low frequency and wave frequency components so that the calculation can use the appropriate part for each load.

Broadly speaking, components of the vessel motion with periods longer than the dividing period will contribute to the low frequency motion, and those components with shorter periods will contribute to the wave frequency motion. The dividing period should ideally be well above the highest period of the significant wave frequency response of your vessel, and at the same time well below the lowest period of significant slow drift response. Review the filter cutoff graphs using your chosen dividing period to obtain an estimate of the period range the filter will require before wave frequency input is fully attenuated.

## Calculation mode

### Time domain

The use of loads based on diffraction analysis data in the time domain is, implicitly, an extrapolation of the behaviour from the linear, small wave height assumptions used by potential theory.

This extrapolation arises because the waves in an OrcaFlex simulation are full size, not infinitesimally small. If vessels follow the example of other OrcaFlex objects, then the vessel response to these full size waves will affect its subsequent position and orientation, and therefore loading, leading to nonlinear behaviour – but the quadratic part of such an extrapolation is already represented by the vessel QTF data. Nonlinear vessel behaviour in OrcaFlex could therefore lead to double-counting of some of the QTF load. The calculation mode allows you to choose how such double-counting should be avoided:

• In filtering mode, diffraction loads are applied using heading frames and filtered heading frames as appropriate. The QTF data are then the only source of quadratic vessel loading, and so are used unmodified by OrcaFlex.
• In QTF modification mode, vessels have the typical nonlinear time domain behaviour. Common second order loads are subtracted from the input QTF data as necessary, in order that the quadratic part of vessel loading is included only once.

The new in version 10.0 notes are a good place to read about the difference between these options. Some initial recommendations can also be presented here regarding this choice:

• The common second order loads used for QTF modification are based on diffraction analysis theory. If your vessel has QTF data from another source, such as loads directly obtained from model tests, then these should be used without modification. Choose the filtering calculation mode in this case.
• The QTF modifications were introduced to address an issue with the filtering mode, in which some cases predicted unrealistically large rotational response. In particular, long slender vessels with relatively low roll stiffness and damping were sometimes predicted to give unrealistically large roll responses in large sea states. If this situation applies to your vessel, then using the QTF modification calculation mode should provide a solution.
• More of the vessel included effects are affected by the filtering of primary motion when the filtering calculation mode is used. For some cases it can be very hard to set a dividing period for the filter, typically when the highest wave period in the applied environment is close to the shortest vessel slow drift response period, such as the system fundamental response period in surge or sway. Under these conditions, the QTF modification calculation mode might provide behaviour which is less sensitive to the chosen filter dividing period.
• The QTF modifications assume that the provided vessel displacement RAOs correspond to the motion used in calculation of the QTFs during diffraction analysis. This assumption can be invalid if the displacement RAOs have been altered in some way, or were obtained from a different source than the other vessel type data. The filtering calculation mode does not make the same assumption, and should be more robust when supplied with data from multiple sources.

In cases where a floating body is well-modelled by diffraction theory, our experience is that both calculation modes give similar behaviour.

The canonical reference for the applicability of diffraction data to large volume structures is the diagram presented by Chakrabarti, 1987, and reproduced in, for example, DNV-RP-C205. This diagram provides a comparison between a chosen characteristic dimension for your structure and the wavelengths of the applied environment. In addition, for time domain analysis, we must consider full size wave conditions. Diffraction analysis assumes that the vessel hull wetted surface and submerged volume do not change significantly. This may no longer be true for vessel behaviour in high seastates, and closely matching results from the two calculation modes cannot always be expected.

### Frequency domain

In the frequency domain, load effects based on the results of diffraction analysis can be applied in either a heading frame, which remains horizontal at all times, or in a frame which rotates out of the horizontal plane. Typical vessel rotations away from horizontal are not large, so it is expected that this choice will not usually make a significant difference to simulation results.

The choice of frame of reference is made via the calculation mode data item. Choosing the frame of application for loading usually makes a more significant difference in time domain analysis, so the options are labelled according to their time domain consequences:

• in filtering mode heading frames, which remain horizontal, are used
• in QTF modification mode, frames are used which will rotate out of the horizontal plane.

### Hydrostatic stiffness input angles calculation

When the filtering calculation mode is used, you must choose how to calculate the roll and pitch angles used as input to the hydrostatic stiffness load. Two options are available: subtraction and orientation.

The two methods are equivalent if the vessel type has zero datum trim angle. For significantly non-zero datum trim angle, we believe that the orientation method is preferable.

### Imposed motion consistent with solver

Determines whether OrcaFlex should modify the imposed velocity and acceleration values to be consistent with the implicit integration scheme. This data is only relevant when the vessel has superimposed motion; or the primary motion is set to prescribed, time history or externally calculated.

## Vessels as child objects

A vessel may be connected as a child object to another parent object. In this case, the vessel's motion is determined by that of the parent object to which it is connected, and many of the calculation options (such as prescribed motion, or any superimposed motion) cannot be permitted. So, for a vessel with a connection other than free, we take away the choices for static analysis and for primary and superimposed time domain motion and impose the following:

• A fixed or anchored vessel does not move at all, so included in static analysis, primary motion and superimposed motion are all none.
• A vessel otherwise connected to a parent has included in static analysis $=$ 6 DOF, primary motion $=$ calculated (6 DOF), and superimposed motion $=$ none.

In the case of frequency domain analysis, child vessels are not permitted: the vessel connection may only be free.