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Figure 5 Rolling Resonance
Rolling motion amplitude of approximately 3 degrees was computed in this study including the fin stabilizers' effect. While the fin stabilizers were very effective, they were under heavy loading as shown in the large magnitude of fin angle up to 15 degrees as shown in Figure c.
Resonance Condition
Furthermore, severe rolling motion of 25 degrees was computed in the simulation runs for the ship under the same sea conditions without fin stabilizers. This result also agrees fairly well with observations after the fin stabilizers stopped working. This severe rolling motion was due to the resonance condition the ship encountered at that time (see Figure 5 Resonance Condition).
The wave encounter time period was 17 seconds under quarter-astern sea conditions while the ship was proceeding at a cruising speed of 18 knots. This caused the resonance condition because the rolling natural period of the ship was also 17 seconds. Figure 5 shows a large magnification factor (roll angle / wave-slope angle) of 5 at the tuning factor of 1.0 under the resonance condition.
Figure 6 V/T Diagram
The effective procedure to avoid this resonance is to reduce the speed, for example, to 9 knots. The wave encounter period reduces to 14 seconds and the tuning factor changes to 1.3 where the magnification factor is reduced to a small value of approximately 1 (see Figure 5). Accordingly, rolling angle is reduced to 4 degrees without fins. It is clearly evident that speed reduction is effective to avoid the resonance and to reduce the rolling motions to a large extent. It is important for shipmasters and deck officers to be familiar with such resonance-avoidance procedure to achieve rolling motion reductions.
V/T Diagram
The effectiveness of the speed reduction is also clearly shown in Takaishi's V/T diagram under the quarter-astern seas as shown in Figure 6 where
V = the ship speed in knots,
T = the wave period in seconds
V/T = (ship speed, knots) / (wave period, Sec.)
X= angle between heading and wave direction.
A point can be plotted in the polar coordinate using V/T and X. When the point is located in the dangerous zone like the one for 18 knots, the ship is under dangerous conditions in the quarter-astern sea or in the following sea. When the ship speed
In 1995, this V/T chart was approved by IMO as the guidance to shipmasters for avoiding the following dangerous situations:
1. Surf-riding and broaching-to
2. Reduction of intact stability caused by riding on the wave crest at midship
3. Synchronous rolling motion
(the case for the cruise ship in this paper)
4. Parametric rolling motion
5. Combination of various dangerous phenomena
CONCLUSIONS
A simulation analysis was made to examine the rolling dynamic behavior of the cruise ship with fin-stabilizers under heavy sea conditions. Results obtained in this study are summarized as follows:
1. Under the heavy quarter astern sea conditions, rolling of the ship at 1 8 knots was computed to be approximately 4 degrees with fin stabilizers working. This agrees well with observations on the ship. While the fin stabilizers were very effective, they were heavily loaded.
2. Under the same weather conditions, rolling of the ship at the speed of 18 knots was computed to be approximately 25 degrees without fin stabilizers. This agrees well with observations after fin stabilizers ceased their function. This heavy rolling was experienced under the resonance condition.
3. Under this situation, a reduction of ship speed is an effective way to reduce rolling to less than 5 degrees, as it moves rolling motions out of the resonance condition (see Figure 5 Rolling Resonance)
4. The V/T diagram also indicates that speed was reduced to 9 knots, the point is located outside of the dangerous zone.
reduction is an effective procedure to reduce ship motions (see Figure 6 V/T Diagram).
ACKNOWLEDGMENT
The authors gratefully acknowledge the discussion given by Prof. Takaishi on the V/T diagram, which he proposed in 1995.
REFFERENCES
H. Eda et al, "Principles of Naval Architecture, Vol III, Controllability," published by Society of Naval Architects and Marine Engineers, 1989
IMO, "Guidance to the Master for Avoiding Dangerous Situations in the Following and Quartering Seas," October 1995
Y. Takaishi, "Dangerous Encounter Wave Grouping Phenomena in Following and Quartering Seas and Application to Operational Guidance," Japan Navigation Society, No. 126, 1995
AUTORS' BIOGRAPHY
Prof. Haruzo Eda has been teaching at US Merchant Marine Academy, Kings Point, New York since 1989. During 1961-89, he was a research scientist and a professor at Stevens Institute of Technology in New Jersey. In 1952-61, he was a research engineer at Ship Research Institute in Tokyo. For these years, he has been actively engaged in research of ship motions. He published four books and numerous papers in the field of ship motions, e.g., "Controllability", Principles of Naval Architecture Vol. III, SANME, 1989.
Dr. F. Eugene Guest is a graduate of the US Merchant Marine Academy and of New York University, School of Education (Ph.D.). He actively sailed as a merchant marine deck officer for ten years and was an Assistant Professor of Nautical Science at US Merchant Marine Academy. He is a former Managing Director of Computer Aided Operational Research Facility at Kings Point, Dr. Guest joined Marinesafety International in 1977, becoming Director of the company in 1983. He has over 26 years experience in simulation-based training and research.
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