- The effect of the relative position of the ship to a wave crest line at the time the rudder is steered:
Fig. 10 shows an example that the rolling amplitude is reduced with the timing of steering in beam sea. In Case (10-a) the rudder starts to rotate at the time the ship locates in wave trough, on the other hand, in Case(10-b) it starts to rotate when the ship locates on the wave slope which lowers the ship's starboard side down. The rolling amplitude in Case(10-a) is obviously smaller than that in Case (10-b). On the other hand, the trajectories of both cases are very similar.
4.4 Summary of the Simulation
So far, some examples of numerical results have been shown and we have tried to add them explanations. To summarize the results, the maximum rolling amplitude that occurs during 180 degrees turning from some initial heading angles and the heading angle at that time of which maximum rolling occurs are described in Table 4. The extreme value occurs in the combination of H/λ=1/20, λ/L=3, Rudder A, ψini=90 degrees. Additionally the maximum rolling amplitude that vary with the timing of steering are also described in Table 5. The extreme value occurs in the combination of H/λ = 1/20, λ/L=2, On the slope (R side down).
The values on these tables show that the maximum rolling amplitudes are influenced by the maneuvering motion in severe sea condition. These facts will be important information to consider the safety operation of a ship in severe sea.
Table 4 Numerical results of the maximum rolling amplitude during 180 deg turning from initial heading angle (Vini=12kt)
*Rudder condition; [A: Original area. δmax=20 deg, B: Original area. δmax=35 deg, C: Large area, δmax=35 deg]
Table 5 Numerical results of the maximum rolling amplitude during 180 degrees turning from initial heading angle (Vini12kt, ψini=-90 deg, δmax=35 deg, Steering in left beam sea)
|Relative position to wave crest line when rudder
|Slope (R. side Up)
|Slope (R. side Down)
In this study, we have investigated the unsteady rolling motion that results from the maneuvering motion in waves by using numerical simulation validated by some experiments, and found out some useful knowledge, they are described below, for safety operation of a small ship.
1) During a ship is turning, the encounter frequency of waves varies from ship's relative speed and direction, so it may generate unpredictable rolling like parametric oscillation, not referred to in this report.
2) In some cases as a ship runs in beam sea, the maximum rolling amplitude during a ship turns through head sea is remarkably larger than turns through following sea.
3) In most cases when a ship runs in head or following sea, the reduction of turning time due to large rudder area makes the rolling amplitude relatively small.
4) In some cases, the proper timing of the start of steering reduces the rolling amplitude during turning and this proper timing varies with wave condition.
These results shows the characteristics of a typical fishing vessel in Japan on some assumed conditions, so there is a possibility that these results will not be applied to general cases. For obtaining more general conclusion, perhaps we need simulations about different type of vessels. Additionally the rolling motion is influenced by the amount of fluid tanks inside and the weight of cargo and so on, therefore the characteristics of rolling motion may vary with the time passage. Taking into account these facts, it is so difficult for operator to predict dangerous situation which occurs after a while. Preparing some sheets, as presented in Fig.6, which shows the characteristics of ship motions due to maneuvering motion in some wave conditions, will be an effective way for safety, operation.
In addition, this study can link the auto-pilot system combining other kinds of information, like information of encounter wave from the radar and the height of ship's center of gravity estimated from the rolling period and the ship position from GPS signal, for safety operation in future.
The authors want to express their sincere thanks to Mr.T.Takayama, Mr.Y.Hirakawa and those students of Ocean-Space-Control-System-Laboratory of Yokohama National University for carrying out the model experiment.
 Hamamoto M, and Kim Y., "New Coordinate System and the Equations Describing Maneuvering Motion of a Ship in Waves", Journal of The Society of Naval Architects of Japan, Vol.173,pp209-220, 1993
 Takezawa S. and Hirayama T., "Advanced Experimental Techniques for Testing Ship Models in Transient Water Waves", 11th Symposium on Naval Hydrodynamics, pp37-54, 1976
 Hirayama T, Nishimura K. and Fnkushima M., "Study on Capsizing Process and Numerical Simulation of a Fishing Boat in Head Waves", Journal of The Society of Naval Architects of Japan, Vol.181,pp169-180, 1997
 Hirayama T, and Nishimura K., "Physical and Numerical Simulation on Capsizing of a Fishing Vessel in Head Sea Condition", Contemporary Ideas on Ship Stability, Elsevier, pp365-377, 2000
The author, K.Nishimura, is a student of the graduate school of Yokohama National University (Department of Ocean and Space Engineering). Mainly he studies the motions and the maneuverability of vessels running in waves.
He holds a Bachelor's degree (Engineering) from Yokohama National University and a Master's degree (Engineering) from the same University. After the Master's course, he got a position of a civil worker belonging to Japan Defense Agency as a ship hull-form designer. Now, he studies at the same university as a doctoral student.