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The peak mooring forces of the container ship as a result of the interaction forces and moment induced by the passing bulk carrier (Table 1 gives details of the ships) while it operates with a speed of 4.0 knots through a water depth of 1.1 times the draft and separated by 0.167 times the ship length are shown in Fig.20 for longitudinal lines and in Fig.21 for lateral lines for a range of values of rope constants. Interaction forces obtained from the present method (Figs.5 to 7) are used in the analysis. The mooring force increases, reaches a maximum and then decreases with increase in rope constant. Here the maximum in longitudinal mooring force occurs at a rope constant of about 100 kN/m and in lateral mooring force at a rope constant of about 400 kN/m. Extreme loadings in the moorings due to passing ships are expected when the apparent period of the interaction force history approximately equals the natural period of the ship-moorings system (here Tn=208s and 380s in surge and sway mode, respectively.) Therefore, the forces experienced by soft moorings, such as synthetic ropes, dues to passing ships, will be larger compared to stiff moorings, such as steel wires. On the other hand, external effects with higher frequency, such as waves and wind fluctuations, will cause more sever loading in stiff moorings. The longitudinal rope tension along with the surge excitation force is plotted in Fig.22 and the lateral rope tension along with the sway excitation force in Fig.23, both for respective maximum force rope constant values (100 & 400 kN/m). The dynamic response of the moored ship must account for the mooring force coming larger than the excitation force, where the amplification is more in surge than in sway. The oscillation in lateral direction dies out faster than that in longitudinal direction, obviously due to the higher damping in sway mode. The form of the vessels have considerable influence on the hydrodynamic interaction sway force and yaw moment [6], which implies that the type of vessels also matters in the analysis of the above problems.
Fig.20. Maximum longitudinal mooring force against rope constant
Fig.21. Maximum lateral mooring force against rope constant
Fig.22. Longitudinal forces on the moored container ship
Fig.23. Longitudinal forces on the moored container ship
Extreme loadings in the moorings due to passing ships are expected when the apparent period of the interaction force history approximately equals the natural period of the ship-moorings system. Therefore, the forces experienced by soft moorings, such as synthetic ropes, due to passing ships, will be larger compared to stiff moorings, such as steel wires. On the other hand, external effects with higher frequency, such as waves and wind fluctuations, will cause more sever loading in stiff moorings.
4. SUMMARY AND CONCLUSION
The hydrodynamic interaction between a moored ship and a moving ship has been studied, where the surge and sway forces and yaw moment are estimated. The estimation of loads on the ropes of a moored container ship due to the hydrodynamic interaction effects induced by a passing bulk carrier has been carried out, by solving the equations of motion. Computations have been done for different ship combinations and have been compared with experimental and other numerical results. The mooring system considered here is a linear one and the equations of motion are uncoupled. The results given here have to be considered as a preliminary one which would give a good insight into the estimation of hydrodynamic interaction forces on a moored ship induced by a passing ship and also its effect on mooring lines.
The conclusions based on the above studies are presented as follows.
1. The character of the forces and the moment, plotted against the relative longitudinal position, is more or less the same for the variations in speeds, passing distances and water depths.
2. The forces and the yaw moment on the moored ship are inversely proportional to the water depth and the lateral separation distance.
3. The form of the ships has more influence on the yaw moment (>50% for the bulk carriers studied here when compared with the idealised parabolic form), where as the increase in sway force is more than 20% and the effect on surge force is 5 to 15%.
4. The studies give a good idea about the moored ship motion due to the hydrodynamic interaction induced by the passage of another ship in its proximity and the consequent mooring line forces.
5. The linear mooring system considered here predicts a higher mooring force than the interaction force. The augmentation can be due to the ship motion dynamics. A further stiffer system resulted in a lower mooring force, where the excursions are expected to be small and hence the ship motion dynamics.
6. Based on the above conclusion, synthetic mooring ropes - being less stiff than steel wires - may experience important dynamic effects due to passing ships. Especially when the apparent period of the interaction is expected to approach one of the natural frequencies of the ship-moorings system, the expected level of the mooring line forces may be exceeded.
ACKNOWLEDGEMENT
This work was part of a project entitled TOHPIC: Tools to Optimise High Speed Craft to Port Interface Concepts, which was carried out in partnership with SSPA, CETEMAR, D'APPOLONIA, SINDEL, METTLE, AMRIE, GU, IFN, MacGREGOR, IST, Stena Line, Dublin Port, Port de Barcelona, Trasmediterranean and funded by the European Commission (Contract No.G3RD-CT-2000-00491). The authors wish to record their gratitude to the Commission in extending financial support for carrying out the numerical part of the above work and to Dr Peter Grundevik, SSPA, Sweden (coordinator of the project), Dr Peter Ottoson and Mr Michael Lee-Anderson. The authors would also like to acknowledge Dr. A. Thavalingam for running some of the computer programs.
REFERENCES
[1] G . F. M. Remery "Mooring Forces Induced by Passing Ships", Offshore Technology Conference Houston, Paper 2066, p.351, 1974
[2] I. W. Dand "Simulation of the Behaviour of a Moored Ship when Passed by Other Ships", National Maritime Institute R 111, 1981
[3] I. W. Dand "Some Measurements of Interaction Between Ship Models Passing on Parallel Courses", National Maritime Institute R108, 1981
[4] K. S. Varyani, R. C. McGregor and P. Wold "Identification of Trends in Extremes of Sway-Yaw Interference For Several Ships Meeting In Restricted Waters", Schiffahrts-Verlag Hansa" Vol 49, pp 174-191, 2002
[5] K. S. Varyani, R. C. McGregor and P. Wold "Empirical Formula to Predict Peak of Force and Moments During Interactions". 13th International Conference on Hydrodynamics in Ship Design, 2nd International Symposium on Ship Manoeuvring. Poland, Sept. 1999
[6] K. S. Varyani and P. Krishnankutty "Hydrodynamic Interaction Between Two Ships", EU Project TOHPIC, Document No 1.3.08.01, May 2002.
[7] M. Vantorre, E. Verzhbitskaya and E. Laforce "Model Test Based Formulations of Ship-Ship Interaction Forces", Schiffstechnik Bd.49-2002/Ship Technology Research, Vol.49, pp 124-141, 2002
[8] M. Vantorre, E. Laforce and E. Verzhbitskaya "Model Test Based Formulations of Ship-Ship Interaction Forces for Simulation Purposes", IMSF - 28th Annual General Meeting, Genova, 2001
[9] OCIMF "Guidelines and Recommendations for the Safe Mooring of Large Ships at Piers and Sea Islands", Oil Companies International Marine Forum, London, 1978
[10] P. Krishnankutty "Computer Simulation of Hydrodynamic Interaction and Mooring Rig Force Analysis", Master's Thesis, Stevens Institute of Technology, New Jersey, USA, 1987
[11] P. Krishnankutty "Hydrodynamic Interaction Forces on a Moored Ship Induced by a Passing Ship", Marine Symposium, May 1997, Bangalore, India, 1997
[12] R. W. Yeung "On the Interaction of Slender Ships in Shallow Water", Journal of Fluid Mechanics, Vol.85, pp 143- 159, 1978
[13] R. W. Yeung and W. T. Tan "Hydrodynamic Interaction of Ships with Fixed Obstacles", Journal of Ship Research, Vol.24, pp 50-59, 1980
[14] S. Wang "Dynamic Effects of Ships Passage on Moored Vessels", Journal of the Waterways, Harbours and Coastal Engineering Division, ASCE, Vol.101, p 247, 1975
AUTHOR'S BIOGRAPHY
Kamlesh Varyani is a Senior Lecturer and a Fellow of the RINA and a Fellow of the Institution of Engineers and Shipbuilders in Scotland and a Chartered Engineer. Since 1990 he has carried out a significant amount of research grant/contract work at the Hydrodynamics Laboratory of The Universities of Glasgow and Strathclyde. His research grants and contracts cover the areas of seakeeping and manoeuvring applied to ships and offshore structures. His current research interests include CFD, slamming, deck wetness, vortex shedding and model testing of ships and offshore structures. He has been involved in several EPSRC projects, industrial contracts with BAE Systems and in TOHPIC, SPIN-HSV and MARNET-CFD EU Projects. He has over 110 publications in various journals, conferences proceedings and research reports covering theoretical and experimental research related to hydrodynamics of ships and offshore structures.
P. Krishnankutty is a Professor in the Department of Ship Technology, Cochin University of Science and Technology, India and is currently on a research assignment, in the area of ship hydrodynamics, with the Department of Naval Architecture and Marine Engineering, Glasgow & Strathclyde Universities, UK.
Marc Vantorre is a Professor in the Division of Maritime Technology, Department of Mechanical Construction & Production, Ghent University, Belgium. His research interests are in the area of ship hydrodynamic interaction and ship manoeuvrability.
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