The ARROW program is a software tool to estimate and display the potential conditions of rolling resonances or high wave impacts on ships due to specific wave encounter situations. Only some data input from the user on ship and waves are needed to provide the qualitative results in a way to identify potential problems and tendencies to derive countermeasures.

According to IMO Guidance to the master for avoiding dangerous situations in following and quartering seas, MSC circular 707, adopted on 19. October 1995 the following phenomena can occur when a ship is affected by high sea state:
- Synchronous rolling motion
- Parametric rolling motion
- Reduction of intact stability caused by riding on the wave crest amidships
- Surf-riding and broaching-to
- Combination of phenomena listed above

Over the last few years several vessels have experienced the dangerous effects of rolling resonance. One result of these harmful encounters is shown beside.
The ARROW polar diagram for these ship and wave conditions would have shown that the ship was in the area of parametric rolling conditions.


Brief Description / Overview of ARROW
The Ship Parameter Input Area allows entering the ships data for stability and to use the pre-calculated or observed data of the ships natural rolling periods as basis for the calculations. The Wave Parameter Input gives the possibility to adjust up to two different wave systems to encounter the ship from different directions and with specific wave periods/length or heights. When more than one wave systems exist, wave interference effects might be taken into account. The Result Display Area is designed as polar diagram where the ships' speed vector position indicates if the ship is in potential dangerous conditions. Different colours and line styles indicate areas for conditions of synchronous or parametric rolling resonance, loss of stability because of successive high wave groups attacks or due to danger of surfriding and broaching-to. These effects can be shown all together when more than one phenomenon appears in parallel or selected separately one by one in the Specify Result Display. The Stability Data Input and Display Window comprises a few data like metacentric height GM, up righting levers GZ for roll angles up to 40░ and the inertia coefficient Cr for rolling motion.

Some Screenshots of ARROW are shown below. At the right hand side of each picture a short extract from the User Manual is provided.

                                                                                                                      
Please click the Thumbnails for enlargement.

Stability Data Input Window

... the calculation of roll resonance and wave impact on a ship is based on the ships natural rolling period which is highly dependant upon the stability data of the ship. The ARROW - Stability Data Window allows the input of the actual stability data ...
Synchronous Roll Resonance

... When selecting this result display option in the ARROW - Display Area the result of the calculation of synchronous rolling resonance effects on the vessel are shown exclusively. Synchronous rolling resonance conditions occur when the ships natural roll periods Tr coincides to the encounter period TE of the wave. They will be shown as stripes in the polar diagram representing the potential conditions for resonance. ...
Parametric Roll Resonance

... The display of the parametric roll resonance effects is shown as a +/- 30░ sector segment for head and stern seas only. The colours have the same meaning as explained for the synchronous resonance. When selecting this result display option in the ARROW - Display Area the result of the calculation of parametric rolling resonance effects on the vessel are shown exclusively. Parametric rolling resonance conditions occur when the ships natural roll periods Tr is equal to half of the encounter period TE of the wave. They will be shown as sector segment in a sector of +/- 30░ for head and stern seas only, representing the potential conditions for this type of resonance. ...
Surf-Riding / Broaching-to

... Selecting this display option, the results of surf-riding and broaching-to effects are shown exclusively.
When a ship is situated on a steep forefront of high wave in following and quartering sea condition, the ship can be accelerated to ride on the wave; this is known as surf-riding. When a ship is surf-ridden, the so-called broaching-to phenomenon may occur, which puts the ship in danger of capsizing as the result of sudden change of ship's heading and unexpected large heeling. ...
High Wave Group Encounter

... When the ship speed component in the wave direction is nearly equal to the wave group velocity, that is a half of the phase velocity of the dominant wave components, the ship will be attacked successively by high waves. The expected maximum wave height of the successive waves can reach almost twice the height of the observed wave of the sea state concerned.
In this situation, the reduction of intact stability together with synchronous rolling or parametric rolling motions or combination of various dangerous phenomena may occur and create the danger of capsize. ...
All Types of Results

... Selecting this option all types of results of roll resonances and wave impacts are shown together in the result display area. All effects are coloured as described in the respective chapters above.
This display mode allows for overall information on all effects which are occurring at the same time and environmental conditions. ...

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