Understanding and Prediction of Ship Motions 

 THIN SHIP THEORY 



Historically, the thin ship idealization was introduced by Michell in his 

 famous study of ship wave resistance. In order to formulate a consistent linear- 

 ized free surface problem for a ship moving at finite speed, it is necessary to 

 assume that there is some identifiable property of the ship which makes the ship 

 produce a very small disturbance, in spite of its moving at an arbitrary finite 

 speed. Michell chose to consider "thin ships," that is, ships with such a small 

 beam/length ratio that they may be pictured as knife-like. 



If we were concerned only with ship motions at zero speed of advance, such 

 problems would not concern us. However, we certainly do not want to restrict 

 ourselves in such a way. Furthermore, a rational theory of ship motions which 

 includes forward speed effects should include the special case of steady forward 

 motion (without time-dependent perturbations). Therefore we are forced to give 

 consideration to the linearization problems which have so disturbed mathemati- 

 cians working on wave resistance theory. 



Michell assumed that, in addition to linearizing the free surface condition, 

 he could replace the boundary condition on the hull by a requirement that there 

 be a certain anti- symmetrical component of velocity normal to the ship center 

 plane. In recent years it has been demonstrated that the latter simplification 

 follows logically from the assumption of small beam, if only we assume that the 

 potential flow can be continued analytically into the hull up to the center plane; 

 it is not a separate linearization.* See, for example, Wehausen (1957) or Stoker 

 (1957). There has been much discussion of this point in recent years, naval 

 architects arguing that there ought to be an improvement in predictions if the 

 hull boundary condition is satisfied exactly — even though the free surface con- 

 dition remains linearized. 



At the risk of offending both naval architects and mathematicians, I must 

 insist that this remains an open question. Certainly, from the point of view of 

 thin ship theory, such a patching-up of procedures is at least inconsistent and 

 could give misleading results, but the grounds for accepting the thin ship ideali- 

 zation are not very secure either. I would hope that some day numerical results 

 may be presented which are based on such a hybrid approach, t Then it may be 

 possible to compare these results with the predictions of the strict thin ship the- 

 ory and with experiments, to find out whether the present apparent shortcomings 

 of the theory can be laid to the simplification of the hull boundary condition, i If 

 such appears to be the case, then we shall have to presume that the premises of 

 thin ship theory are at fault. 



*Newman has claimed that even the assumption of the possibility of analytic con- 

 tinuation is not needed. See p. 39, Newman (1961). 



tWe had had hopes of obtaining just such results from the work at the Douglas 

 Aircraft Co. See Smith, Giesing, and Hess (1963). Apparently the problem is 

 still too complicated for present day methods, even with computers such as the 

 IBM 7090. 



^Before this is possible, there will have to be a tremendous improvement in our 

 understanding of the experiments as well. 



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