Seakeeping Dialog - Regular Data Tab

The vessel Response Amplitude Operators (RAO's) are calculated for the six degrees of freedom motions:

• surge

• sway

• heave

• roll

• pitch

• yaw

They are calculated over a range of speeds (which may be supplied here) and at each wave heading and frequency (or wavelength) specified on Dynamic Positioning Data - General.

In addition to the vessel sections, defined up to the draught given in Seakeeping Dialog - Loading Condition Tab and the weight distribution given on the same page, certain other information is required which can change the vessel responses, namely:

• Formulation for calculating the RAO's

• Non-Linear Roll Damping coefficients

• Fin Control Coefficients

Speeds

Up to 10 speeds (knots) may be supplied. The short term calculations (regular and irregular responses) are then automatically calculated for each of these speeds.

RAO Calculations

The calculation of the vessel wave excitation forces has been based on the Vugt’s References 45 formulation, which is basically a modification of the more widely known Scores formulation.

The differences in the two methods are solely in the speed-dependent contributions, with the Vugt’s formulation including terms containing (), where is the wave frequency and we the wave encounter frequency.

However, for certain combinations of vessel speed, wave heading and wave frequency, the value for the encounter frequency becomes zero, and hence these terms grow rapidly. In these cases, it is seen that the wave excitation, and hence the vessel RAO's are over-predicted.

Since the Scores formulation does not include such terms, this method does not cause the large peaks occasionally seen when viewing the RAO's. Therefore, if your calculations include such combinations, it is recommended that they choose the Scores formulation.

Import / Export

The short term response amplitude operators may be output to a standard ASCII file, or indeed imported from a similar file. The format of this file is given in RAO File Structure.

This facility has been added to give you increased flexibility over the seakeeping calculations:

The RAO's must be supplied for the same speed range as defined in the speeds grid, and at the same wave frequencies and headings as defined in the Dynamic Positioning Data - General Tab, under Conventions.

Modification of calculated RAOs

The wave exciting forces are calculated using a well known method by Vugt’s References 45. However, for very small wave encounter frequencies, this formulation may cause large peaks in the excitation forces, and hence large peaks in the vessel RAOs, including the added resistance, shear forces and bending moments.

This phenomenon occurs only in following / stern quartering seas, at higher vessel speeds, when the wave and ship travel together.

In such cases, you may export the RAOs, smooth out the peaks using their own smoothing algorithm, and re-import the altered values, allowing the irregular responses to be calculated using a more realistic set of RAOs.

Note:
These peaks tend to be in the higher frequency range where the wave energy is minimal. However, when combining the RAOs and the spectrum, large errors may be seen in the irregular response RMS values due to the extremely large RAO values. In such cases, setting the RAO values to zero would produce a more accurate set of irregular responses.

Non-Linear Roll Damping

However, if you have available roll damping model tests, then coefficients may be included into the roll equation (1) directly as:

Unchecking the Compute Damping box, therefore highlights the B1 and B2 input boxes, and you should input the values as defined in Equations (2) and (3) below.

Fin Control Coefficients

Hydro can also analyze the effect of active fin stabilizers. The majority of the data required is defined on Appendages Dialog - Stabilizer Fins Tab.

The seakeeping calculations assumes there are two fins symmetrical about the centerline.

In addition the following data is also required:

Typical values would be: