ABSTRACT 



To predict motions of SWATH ships in following seas, 

 especially when the encounter frequency is small, unified 

 slender-body theory has been applied. The longitudinal 

 interaction term is computed and added to the results of 

 the strip theory as a correction term. The added mass 

 coefficients are computed to be much larger than those 

 from strip theory, while damping coefficients are 

 slightly less than two-dimensional results. There is im- 

 provement for heave motion for a limited range of fre- 

 quencies, but the pitch motion is generally poor. To 

 improve these results further, the two-dimensional potential 

 should be solved by the multipole expansion method rather 

 than by the Frank close-fit method. 



ADMINISTRATIVE INFORMATION 

 This study was performed under the General Hydromechanics Research Program and 

 was authorized by the Naval Sea Systems Command, Hull Research and Technology Office. 

 Funding was provided under Program Element 61153N, Task Area SR 0230101, and Work 

 Unit 1572-031. 



INTRODUCTION 



An analytical method to predict the motions of SWATH ships has been developed 



1* 

 by Lee. The numerical results computed by this method provide good correlation 



with model test results for moderate speed ranges. The present author has improved 



the prediction of heave and pitch motions in head seas by adding surge effect to 



2 

 the pitch exciting moment and by correcting the viscous damping terms. 



However, in following seas correlation between the analytical method based on 

 strip theory and model test results is not satisfactory. In particular, when the 

 SWATH ship moves almost as fast as the wave celerity, the encounter frequency be- 

 comes very small and application of strip theory is not valid. The fundamental 

 assumption of strip theory is that the frequency is far larger than the product of 



the longitudinal gradient of the body surface and the forward speed. 



3 

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



He has developed the unified slender-body theory which is valid for all frequencies 



*A complete listing of references is given on page 75, 



1 



