Nowadays, most of the dynamic research on planing ships has been directed towards analyzing the ships motions in either 3-DOF (degrees of freedom) mode in the longitudinal vertical plane or in 3-DOF or 4-DOF mode in the lateral vertical plane. For this reason, the current authors have started a research program of describing the dynamic behavior of planing ships in a 6-DOF mathematical model. This program includes the developing of a 6-DOF computer simulation program in the time domain. This type of simulation can be used for predicting the response of these planing vessels to the environmental disturbances during high-speed sailing. In this paper, the development of the mathematical model will be presented. Furthermore, a discussion will be offered about the use of these static contributions in a time domain simulation for modeling the behavior of planing crafts in regular waves. 1. Introduction Prediction of planing craft motion is one of the main computational challenges in marine engineering. Due to the involved computational time, computational fluid dynamics is very expensive. Experimental works are also very costly. Therefore, several researchers have tried to present mathematical models which are very easy and economical. In the last decades, two branches of mathematical models have been developed which are in two or three degrees of freedom. First branch was developed by Savitsky [1]. Savitsky’s model has not been developed extensively. For example, it cannot be applied to the planing motion in irregular waves, and it is also difficult to use it to obtain time domain simulation. However, second branch which was developed by Martin [2] has been implemented by many authors. In reality, Martin’s [2] model was in frequency domain. Zarnick [3] worked on this model and performed time domain calculations. Later, Zarnick [4] developed Martin’s model even further for planing craft motion in irregular waves. He compared his results with the experimental findings of Fridsma [5, 6] and found his model to be in favorable agreement with the experimental data. However, Zarnick’s model had some restrictions which had been resolved by some researchers. In fact, after several decades, a model which was initially developed by Zarnick is still a reliable tool for planing craft motion. Keuning [7] extended Zarnick’s [3, 4] model to incorporate a formulation for the sinkage and trim of the ship at high speeds. He also studied the hydrodynamic lift distribution along the length of the ship with nonlinear added mass and wave exciting force in both regular and
References
[1]
Savitsky, “Hydrodynamic design of planing hull,” Marine Technology, vol. 1, no. 1, pp. 71–95, 1964.
[2]
M. Martin, “Theoretical prediction of motions of high-speed planing boats in waves,” Journal of Ship Research, vol. 22, no. 3, pp. 140–169, 1978.
[3]
E. E. Zarnick, “A non-linear mathemathical model of motions of a planning boat in regular waves,” Tech. Rep. DTNSRDC-78/032, David Taylor Naval Ship Reasearch and Development Center, Bethesda, Md, USA, 1978.
[4]
E. E. Zarnick, “A non-linear mathemathical model of motions of a planning boat in irregular waves,” Tech. Rep. DTNSRDC/SPD 0867-01, David Taylor Naval Ship Reasearch and Development Center, Bethesda, Md, USA, 1979.
[5]
G. Fridsma, “A systematic study of the rough-water performance of planning boats,” Tech. Rep. 1275, Davidson Laboratory, Stevens Institue of Technology, Hoboken, NJ, USA, 1969.
[6]
G. Fridsma, “A systematic study of the rough-water performance of planning boats(irregular waves—part II),” Tech. Rep. 11495, Davidson Laboratory, Stevens Institue of Technology, Hoboken, NJ, USA, 1971.
[7]
J. A. Keuning, The nonlinear behaviour of fast monohulls in head waves [Ph.D. thesis], Technische Universiteit Delft, Delft, The Netherlands, 1994.
[8]
J. D. Hicks, A. W. Troesch, and C. Jiang, “Simulation and nonlinear dynamics analysis of planing hulls,” Journal of Offshore Mechanics and Arctic Engineering, vol. 117, no. 1, pp. 38–45, 1995.
[9]
R. H. Akers, “Dynamic analysis of planning hulls in the vertical plane,” in Proceedings of the Meeting of the New England Section of the Society of Naval Architects and Marine Engineers (SNAME '99), Ship Motion Associates Portland, Maine, April 1999.
[10]
K. Garme and A. Rosén, “Time-domain simulations and full-scale trials on planing craft in waves,” International Shipbuilding Progress, vol. 50, no. 3, pp. 177–208, 2003.
[11]
K. Grame and A. Rosen, Modeling of planning craft in waves [Ph.D. thesis], Royal Institue of Technology KTH, Department of Aeronautical and Vehicle Engineering, Stockholm, Sweden, 2004.
[12]
A. van Deyzen, “A nonlinear mathematical model of motions of a planning monohull in head seas,” in Proceedings of the 6th International Conference on High Performance Marine Vehicles (HIPER '08), Naples, Italy, September 2008.
[13]
L. Sebastianii, D. Bruzzone, and P. Gualeni, “A practical method for the prediction of planing craft motions in regular and irregular waves,” in Proceedings of the 27th International Conference on Offshore Mechanics and Arctic Engineering (OMAE '08), pp. 687–696, Estoril, Portugal, June 2008.
[14]
H. Sun and O. M. Faltinsen, “The influence of gravity on the performance of planing vessels in calm water,” Journal of Engineering Mathematics, vol. 58, no. 1–4, pp. 91–107, 2007.
[15]
S. B. Rao and C. K. Shantha, Numerical Methods: With Programs in Basics, Fortran, Pascal, and C++, Universities Press, India, Revised edition, 2004.
