Coupled heave and pitch motions of planing hulls at non-zero heel angle

Abstract Current paper presents a mathematical model based on 2D-asymmetric wedge water entry to model heave and pitch motions of planing hulls at non-zero heel angles. Vertical and horizontal forces as well as heeling moment due to asymmetric water entry are computed using momentum theory in conjunction with added mass of impact velocity in vertical and horizontal directions. The proposed model is able to compute sway and yaw forces, roll moment, as well as heave and pitch motions in calm water and regular waves. Validity of the proposed model is verified by comparing the results against existing experimental data in both symmetric and asymmetric conditions. Ultimately, different parametric studies are conducted to examine the effects of non-zero heel angle on dynamic vertical motions. The resulting sway and yaw forces due to asymmetric motion are also derived and effects of heel angle on these side forces are investigated.

[1]  Parviz Ghadimi,et al.  Initiating a Mathematical Model for Prediction of 6-DOF Motion of Planing Crafts in Regular Waves , 2013 .

[2]  Parviz Ghadimi,et al.  Analytical solution of wedge water Entry by using Schwartz-Christoffel Conformal Mapping , 2011, Int. J. Model. Simul. Sci. Comput..

[3]  Walter E. Klosinski,et al.  DIRECTIONAL STABILITY TESTS OF TWO PRISMATIC PLANING HULLS; FINAL REPT , 1994 .

[4]  Daniel Savitsky,et al.  High-speed Hydrodynamic Characteristics of a Flat Plate and 20 Degrees Dead-rise Surface in Unsymmetrical Planing Conditions , 1958 .

[5]  P. Ghadimi,et al.  Simulation of 2D symmetry and asymmetry wedge water entry by smoothed particle hydrodynamics method , 2015 .

[6]  P. Ghadimi,et al.  Finding the best combination of numerical schemes for 2-D SPH simulation of wedge water entry for a wide range of deadrise angles , 2014 .

[7]  Michael G. Morabito,et al.  Prediction of planing hull side forces in yaw using slender body oblique impact theory , 2015 .

[8]  Karl Garme.  IMPROVED TIME DOMAIN SIMULATION OF PLANING HULLS IN WAVES BY CORRECTION OF THE NEAR-TRANSOM LIFT , 2005 .

[9]  Parviz Ghadimi,et al.  Study of water entry of circular cylinder by using analytical and numerical solutions , 2012 .

[10]  Parviz Ghadimi,et al.  Steady performance prediction of a heeled planing boat in calm water using asymmetric 2D+T model , 2017 .

[11]  Armin W. Troesch,et al.  Initial water impact of a wedge at vertical and oblique angles , 2004 .

[12]  Key Pyo Rhee,et al.  Theoretical prediction of running attitude of a semi-displacement round bilge vessel at high speed , 2013 .

[13]  P. Ghadimi,et al.  Effect of flat deck on catamaran water entry through smoothed particle hydrodynamics , 2016 .

[14]  P. R. Payne.  Recent developments in “added-mass” planing theory , 1994 .

[15]  Ermina Begovic,et al.  Experimental seakeeping assessment of a warped planing hull model series , 2014 .

[16]  Key Pyo Rhee,et al.  Design of high-speed planing hulls for the improvement of resistance and seakeeping performance , 2013 .

[17]  A. C. Fairlie-Clarke,et al.  An experimental investigation into the constant velocity water entry of wedge-shaped sections , 2008 .

[18]  Armin W. Troesch,et al.  Asymmetric Hydrodynamic Impact and Dynamic Response of Vessels , 1999 .

[19]  Heinrich Söding,et al.  Motion Simulations for Planing Boats in Waves , 2003 .

[20]  Parviz Ghadimi,et al.  Development of a mathematical model for simultaneous heave, pitch and roll motions of planing vessel in regular waves , 2013 .

[21]  Yasumi Toyama,et al.  Two-dimensional Water Impact of Unsymmetrical Bodies , 1993 .

[22]  P. Ghadimi,et al.  NUMERICAL SIMULATION OF WATER ENTRY OF DIFFERENT ARBITRARY BOW SECTIONS , 2014 .

[23]  Carolyn Q. Judge.  Empirical Methods for Predicting Lift and Heel Moment for a Heeled Planing Hull , 2014 .

[24]  Daniel Savitsky,et al.  Hydrodynamic Design of Planing Hulls , 1964 .

[25]  Parviz Ghadimi,et al.  An analytical procedure for time domain simulation of roll motion of the warped planing hulls , 2016 .

[26]  Mohammad A. Feizi Chekab,et al.  Investigation of three-dimensionality effects of aspect ratio on water impact of 3D objects using smoothed particle hydrodynamics method , 2016 .

[27]  Luca Sebastiani,et al.  A Practical Method for the Prediction of Planing Craft Motions in Regular and Irregular Waves , 2008 .

[28]  Armin W. Troesch,et al.  Simulation and Nonlinear Dynamics Analysis of Planing Hulls , 1993 .

[29]  O. Faltinsen,et al.  Water entry of two-dimensional bodies , 1993, Journal of Fluid Mechanics.

[30]  Yoshiho Ikeda,et al.  LONGITUDINAL MOTION OF A SUPER HIGH-SPEED PLANING CRAFT IN REGULAR HEAD WAVES , 2000 .