3.1. Basic Consideration 



It is much to the credit of E. Lewis [61] that he had the courage to recommend 

 rules for design derived from elementary theoretical findings including considerations 

 yielded by the modern irregular seaway theory. His paper contributed numerous results 

 of immediate value for practice. 



Although we accept E. Lewis' work as basic, there are some reasons to recon- 

 sider the heave and pitch problem. 



1. E. Lewis intentionally does not consider the influence of the longitudinal 

 displacement distribution (more correctly, the shape of the load waterline) on the 

 exciting forces for given main dimensions of the ship. This is, however, one of the few 

 dependencies which can be investigated with some confidence within the range of 

 validity of the Froude-Krylov hypothesis. 



2. The present knowledge of damping properties admits of more definite state- 

 ments although we are still far away from an exhaustive solution of the problem. 



3. Objections have been raised against the choice of Taylor's displacement- 

 length ratio by several writers including the present one. Let us consider the question 

 once more. 



The use of the parameter D/L 3 , consecrated by resistance research, has 

 undoubtedly led to a preliminary orientation in the new field, since for fixed displace- 

 ment, this main form parameter successful shows the importance of length. For 

 detailed work, however, one should avoid merging several characteristic form parameters 

 into a single one. 



The present survey is based on the simple Equations (1) and (2) and their solu- 

 tion for forced motions. Exciting terms can be corrected using the relative motion 

 concept. 



For our present discussion, which remains within the linear range, the wave 

 length A is the most interesting characteristic, although height (steepness or slope) 

 obviously becomes equally important when limiting values or accelerations have to be 

 considered. 



Let us first collect some basic, useful formulae. 



Frequencies of encounter: w * = coo*(l — Fcoo* cos x) (17) 



wo* 

 Tuning factor: A = (1 — Fu> * cos x) (18) 



z m * = — = # 2 (AW z (k z ,A*) 



f ' m 



Amplitude ratios: (19) 



Phase lag: tan £ = (20) 



1 - A2 



Damping: k, = (21) 



P VV' z A w g 



1 

 Magnification factor: n = (22) 



