4 

 Newman recently applied slender-body theory to the problem of predicting ship 



motion. He has developed a unified slender-body theory and applied it to the compu- 

 tation of added-mass and damping coefficients. Newman and Sclavounos have computed 

 added-mass and damping coefficients for surface ships, and their numerical results 

 agree well with the three-dimensional results for a surface ship when the forward 

 speed is zero. For the case of nonzero forward speed, the agreement is not as good 

 as for zero speed. 



The author has previously applied the unified slender-body theory to the compu- 

 tation of motions of SWATH ships in following seas. This resulted in an improve- 

 ment in predicting the effects of added-mass and damping coefficients, but a rather 

 inconsistent improvement in motion predictions. Furthermore, the numerical handling 

 of the hydrodynamic singularity was deficient; this singularity problem has been 

 corrected. Numerical computations in following seas are repeated in this report. 



The unified slender-body theory is here applied to improve the prediction of 

 motion of high-speed SWATH ships in head seas. Two-dimensional theory is applied 

 in the inner region and three-dimensional theory is applied in the outer region of 

 the hydrodynamic flow domain. The matching process is taken in an intermediate 

 region, and the correction terms are added to the results of the strip theory. The 

 numerical results are compared with those of strip theory and experiment. An 

 improvement in predicting hydrodynamic coefficients has been achieved, but a similar 

 improvement has not been obtained in the motion results. 



EQUATIONS OF MOTION 



COORDINATE SYSTEMS 



Two coordinate systems are defined: the first (x ,y ,z ) is fixed in space, 

 3 o o o o 



and the second 0(x,y,z) is fixed with respect to the ship which moves with a forward 



speed U along the positive x axis. The Oz axis is directed vertically upward, 



o o 



and the Ox axis is positive in the direction of the ship's forward velocity (Figure 

 1) . The Oxy-plane is in the plane of the undisturbed free surface. The two 

 coordinate systems coincide when the ship is at rest at time zero. 



Using the slender-body theory, the length of the ship is assumed to be far 

 larger than the beam or the draft. We separate the fluid domain (y,z) into two 

 regions: the outer region where (y,z) is of the order of the length of the ship, 

 and the inner region where (y,z) is of the order of the beam or draft. In the outer 



