The high speeds, small trim angles, and shallow drafts of planing hulls produce large changes in vessel wetted surface which, in turn, lead to significant hydrodynamic and dynamic nonlinearities. Due to the complex nonlinearities of this type of craft, naval architects and planing boat designers tend to rely upon experimental tests or simulation for guidance. In order for simulation to be an effective design tool, a fundamental understanding of the system’s dynamic characteristics is required. This paper describes a developing methodology by which the necessary insight may be obtained. A demonstration of the combined use of modern methods of dynamical system analysis with simulation is given in the evaluation of the vertical motions of a typical planing hull. Extending the work of Troesch and Hicks (1992) and Troesch and Falzarano (1993), the complete nonlinear hydrodynamic force and moment equations of Zarnick (1978) are expanded in a multi-variable Taylor series. As a result, the nonlinear integro-differential equations of motion are replaced by a set of highly coupled, ordinary differential equations with constant coefficients, valid through third order. Closed-form, analytic expressions are available for the coefficients (Hicks, 1993). Numerical examples for all first-order and some second-order terms are presented. Once completely determined, the coefficient matrices will serve as input to path following or continuation methods (e.g., Seydel, 1988) where heave and pitch magnification curves can be generated, allowing the entire system response to be viewed. The branching behavior of the solutions resulting from a variation of the center of gravity is examined in detail. These studies of the second-order accurate model show the potential of the method to identify areas of critical dynamic response, which in turn can be verified and explored further through the use of the simulator.

Issue Section:
Research Papers
Topics:
Hull, Nonlinear dynamics, Simulation, Architects, Boats, Center of mass, Design, Differential equations, Dynamic response, Dynamic systems, Equations of motion, Fluid-dynamic forces, Magnification, Vessels
1.
Blount, D. L., and Codega, L. T., 1991, “Dynamic Stability of Planing Boats,” Fourth Biennial Power Boat Symposium, Society of Naval Architects and Marine Engineers, Miami, FL; also, 1992, Marine Technology, Vol. 29, No. 1.
2.
Codega, L., and Lewis, J., 1987, “A Case Study of Dynamic Instability in a Planing Hull,” Marine Technology, Vol. 24, No. 2.
3.
Cohen, S. H., and Blount, D. L., 1986, “Research Plan for the Investigation of Dynamic Instability of Small High-Speed Craft,” Trans. of SNAME, Vol. 94.
4.
Doctors, L. J., 1985, “Hydrodynamics of High-Speed Craft,” University of Michigan Department of Naval Architecture, Report 292, Ann Arbor, MI.
5.
Doedel, E., 1986, “AUTO: Software for Continuation and Bifurcation Problems in Ordinary Differential Equations,” CalTech, Pasadena, CA.
6.
Hicks, J. D., 1993, “Analysis Method for Planing Hull Vertical Motions,” thesis, Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI.
7.
Martin, M., 1978a, “Theoretical Determination of Porpoising Instability of High-Speed Planing Boats,” Journal of Ship Research, Vol. 22, No. 1.
8.
Martin, M., 1978b, “Theoretical Prediction of Motions of High-Speed Planing Boats in Waves,” Journal of Ship Research, Vol. 22, No. 3.
9.
Meyers, W. G., Applebee, T. R., and Baitis, A. E., 1981, User’s Manual for the Standard Ship Motion Program, SMP, David W. Taylor Naval Ship Research and Development Center Report No. DTNSRDC/SPD-0936-01, Sept.
10.
Payne, P. R., 1990, Boat 3D—A Time-Domain Computer Program for Planing Craft, Payne Associates, Stenensville, MD.
11.
Savitsky, D., 1964, “Hydrodynamic Design of Planing Hulls,” Marine Technology, Vol. 1, No. 1.
12.
Savitsky, D., 1968, “On the Seakeeping of Planing Hulls,” Marine Technology.
13.
Savitsky, D., and Brown, P. W., 1976, “Procedures for Hydrodynamic Evaluation of Planing Hulls in Smooth and Rough Water,” Marine Technology, Vol. 13, No. 4.
14.
Seydel, R., 1988, From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis, Elsevier, New York, NY.
15.
Troesch, A. W., 1992, “On the Hydrodynamics of Vertically Oscillating Planing Hulls,” Journal of Ship Research.
16.
Troesch
 
A. W.
, and
Falzarano
 
J. M.
, 1992, “
Modern Nonlinear Dynamical Analysis of Vertical Plane Motion of Planing Hulls
,” presented at the SNAME Great Lakes and Great Rivers Section Meeting, Cleveland, OH, January 23; also,
1993
,
Journal of Ship Research
, Vol.
37
, No.
3
, Sept., pp.
189
–
199
.
17.
Troesch, A. W., and Hicks, J. D., 1992, “The Efficient Use of Simulation in Planing Hull Motion Analysis,” ASNE High Performance Marine Vehicles Proceedings, Washington, DC.
18.
Vorus, W. S., 1993, “Hydrodynamic Impact and Penetration of Flat Cylinders,” submitted to Journal of Fluid Mechanics.
19.
White, J. A., and Savitsky, D., 1988, “Seakeeping Predictions for USCG Hard Chine Patrol Boats,” presented at the New York Metropolitan Section of SNAME, June 16.
20.
Zarnick, E. E., 1978, “A Nonlinear Mathematical Model of Motions of a Planing Boat in Regular Waves,” DTNSRDC Report 78/032.
21.
Zhao, R., and Faltinsen, O., 1992, “Water Entry of Two-Dimensional Bodies,” Seventh International Workshop on Water Waves and Floating Bodies, Val de Reuil, France, May.
This content is only available via PDF.
Copyright © 1995
 by The American Society of Mechanical Engineers
You do not currently have access to this content.