Understanding and Prediction of Ship Motions 



validity. Fortunately, the experiments of Davis and Zarnick (1964) with a pitch- 

 ing and heaving aircraft carrier at zero speed show good agreement with calcu- 

 lations based on the very simple, lowest order theory developed by Newman, and 

 there is some hope that the higher order theory outlined here will still give good 

 results even when resonance phenomena become more important. 



It may be well to recall again (see the Introduction) how the slender body 

 approach rectifies the difficulty of the Peters-Stoker thin ship model. In the 

 latter, the Froude-Krylov excitation, the hydrostatic restoring force, and the 

 ship inertia force were all of the same order of magnitude, and damping and 

 added mass forces were of higher order of magnitude. Because of the presence 

 of "spring forces" and inertia forces and the absence of damping, the system 

 had resonances with unbounded amplitudes of motion. In the slender body the- 

 ory, the mass and thus the inertial reactions are raised to a higher order in 

 terms of the small parameter, while the restoring forces are unchanged in 

 order of magnitude. Without the inertia terms, there is no resonance at all in 

 the lowest order theory, and when inertia does appear in higher order terms, 

 damping also enters in. 



There is one other difference between this slender body approach and the 

 Peters-Stoker theory which may be mentioned. In the latter, it was assumed 

 that the slope of the incident waves was small, of the same order of magnitude 

 as the (small) beam/length ratio. In the slender body theory, wave height (or 

 slope) remains an independent parameter, and all of the above results may be 

 considered as part of a homogeneous first order theory in terms of such a pa- 

 rameter. However, this parameter must be small compared with e, the slen- 

 derness parameter. 



REFERENCES 



The references listed here are limited to those mentioned in the text, with 

 a few exceptions. Five of the publications are marked with an asterisk; these 

 have extensive bibliographies which may be of further interest to the reader. 



G. Chertock, 1962. General Reciprocity Relation. J. of the Acoustical Society 

 of America, 34, 989. Reprinted as David Taylor Model Basin Report 1663 



L. J. Cote, 1954. Certain Problems Connected with the Short Range Prediction 

 of Sea Surface Height. New York University College of Engineering Re- 

 search Division Technical Report No. 4 



W. E. Cummins, 1962. The Impulse Response Function and Ship Motions. 



Schiffstechnik, 9, 101-109. Reprinted as David Taylor Model Basin Report 

 1661 



W. E. Cummins and W. E. Smith, 1964. Pulse Methods for Determining Ship 

 Motions. Fifth ONR Symposium on Naval Hydrodynamics, to be published 



221-249 O - 66 



65 



