2.2 Interesting observations

　

 How could the unstable behaviour and excessive roll of some ships be explained? In order to find some answers one of the extreme ships (ShipA) and one more normal (ShipB) were selected for further studies. Some data for these ships are given in the following table.

　

　

 Time histories of different variables are given below. From fig 7 the difference in overshoots between the ships can be seen, i.e. the overshoot for ShipA is 59°while it is 20°for ShipB, which is more normal and within the criteria of IMO resolution A751(25°).

　

　

 Of course a large roll could be expected for ShipA relative to ShipB due to the low GM as given in fig 8. However that could not be the only reason. For instance, why is the roll so much larger in spite of the lower speed?

　

　

 Based on a real case with a capsizing ship it was concluded that the relatively low GM in combination with an unusual GZ curve with a poor initial stability could explain the remarkable roll angle leading to the capsizing (see ref 2). However, the GZ curve of ShipA is quite normal with a good initial stability.

　

 Another idea was that large drift angles generally create large roll moments. Again the relatively small difference in drift angle (fig 9) is not likely to explain the large difference in roll.

　

　

 It is generally known that a forward trim has a negative effect on course stability. The unusual stern shape of ShipA, a kind of extreme barge type, should make the ship trim by the bow in combination with heel from pure hydrostatic point of view. But how does the trim change during the zig-zag test?

　

 Fig 10 gives the trim variation for the two ships from the model tests and here we can see an interesting difference. ShipA is trimming by the bow at the maximum heel after abt 50 sec while ShipB is trimming by the stern. For the approach condition both ships have a small forward dynamic trim although the static trim is zero.

　

　

 Of course the yaw rate in combination with a high centre of gravity is the main contributor to the roll moment. In fig 11 the yaw rate it can be seen that ShipA (---) is turning much faster than the normal ShipB (―) in spite of the lower ship speed (fig 12). The unstable behaviour of ShipA is not only confirmed by the large overshoot and the large roll but also by the larger relative speed reduction in the zig-zag test.

　

　

　

 The empirical formulas (1) and (2) presented in this paper for estimation of the maximum roll and 1^st overshoot in the 20/20°zig-zag test are relatively simple only considering a few parameters that generally are easily available. Thus the result should not be expected to be absolutely correct. This method should rather be seen as a tool primarily to be used during the design phase to assess the dynamic stability of a ship but also for instance by ship officers to get an indication of the behaviour of a certain ship at different load conditions and speed.

　

 Only even keel conditions are considered in this study. Unfortunately the effect of trim is not included although it is a well-known fact that a stern trim improves course-stability. Of course there are many other parameters and factors that would be important for a study of this kind, i.e. stem shape, LCB, rudder area and type, etc. However such data was not available for all ships in this study and would not always be available for practical use.

　

 Model tests were also carried out with the most extreme ships fitted with larger rudders or course stabilising fins of realistic design and size. Only marginal improvements of the unstable behaviour were accomplished. Thus it was concluded that the most important factor next to the GM and stern shape would be the length to beam ratio or the slenderness ratio.

　

 For some reason very limited full-scale experience of this phenomenon is known to the author. Maybe ships are not operated at the critical tested conditions or the operator avoids manoeuvres that make the ship heel excessively. Or could it be that ship owners do not want to talk about this kind of problem.

　

 Nevertheless it is important to be aware of this phenomenon and try to avoid any hazards because of it. One first warning could be given by a simple check using the method described in this paper.

　

[1] Eda Haruzo: "Rolling and Steering Performance of High Speed Ships", Proc. of Thirteenth Symposium on Naval Hydrodynamics, pp. 427-439, Tokyo 1980

[2] Källström C G & Ottosson P: "The Generation and Control of Roll Motion of Ships in Close Turns", Fourth International Symposium on Ship Operation Automation. IV, E Volta (editor), North Holland Publishing Company, IFIP 1983

[3] Oltman Peter: "Roll - An often neglected element of manoeuvring", Proc of MARSIM'93, pp.463-471, 1993

　

 Peter Trägårdh graduated as Master of Science in Naval Architecture from the Royal Institute of Technology in Stockholm in 1971. He has been at SSPA since then, working with research as well as commercial projects within most aspects of ship hydrodynamics but with special attention to ship manoeuvring including model testing as well as simulation work. For some time he gained some practical full-scale experience working with some Swedish shipyards (1979-1985). Member of the 23^rd and 24^th ITTC Manoeuvring Committees (1999-). Email address: peter.tragardh@sspa.se