CHALLENGE TO BETTER AGREEMENT BETWEEN THEORETICAL COMPUTATIONS 

 AND MEASUREMENTS IN SHIP HYDRODYNAMICS 



INTRODUCTION 



There is a great difference between the idea of engineering and 



that of mathematics. The substantial importance in engineering is the 



practical utility. Any theories cannot become useful unless they lead to 



results which are faithful representations of actual phenomena. 



In natural sciences like physics or chemistry, one may be contented 

 with qualitative agreement between theoretical predictions and observa- 

 tions, but in engineering, merely qualitative agreement is not a sufficient 

 condition of the practical usefulness. The agreement should be quantita- 

 tive within required accuracy. Mathematics, on the other hand, emphasizes 

 logical rationality. If one considers an approximation, the rigorous 

 mathematical idea requires that the simplification should be consistent 

 within itself throughout the approximation. However, we often encounter 

 cases that mathematical rationalism contradicts the practical usefulness. 

 We know quite a few cases that a mathematical theory, with all its rational 

 construction, yields rather unrealistic results when compared with the 

 actual phenomena. On the other hand, there are a number of cases that 

 deviation from the rational formulation can result in much better agree- 

 ment with measurements. Generally speaking, such inconsistent approaches 

 are not necessarily safe, because their justification is hardly obtained 

 from the purely theoretical point of view. However, the utility of this 

 kind of approximate method can be appreciated in the practical appli- 

 cation, since any theory which has failed to give correct predictions is 

 almost useless even though it has a complete logical construction from the 

 mathematical point of view. 



The present lecture intends to illustrate how the deviation from the 

 mathematical rationality can improve the agreement with measured results 

 and how the mathematical theory may be revised for practical usefulness. 

 Whether any inconsistent approach can become really useful or not depends 

 greatly upon the engineer's intuition. 



The title of the lecture can cover very wide aspects, but I will 

 confine topics only in problems of free surface flow, because it is the 



