SHIP MOTIONS 



211 



possible to use mailahlc small-c:ipacit\' computing 

 machines. 



It is recommended that the foregoing programming 

 first be made for the solution of linearized ef|Uutions 

 with constant coefhcients for immediate practical ap- 

 plication. A research program also is recommended foi- 

 solution of ecjuations with varialilc coefficients (step- 

 by-step integration). 



The foregoing discussion referred particularly to heav- 

 ing-pitching motions in regular \va\-es. The results 

 should be generalized in order to represent ship motions 

 in a typical irregular sea. This can be done by statis- 

 tical methods and a suitable computational procedure. 



It should be rem(>mbered that in ol)li(|ue seas the 

 entire six-mode motion (seven degrees of freedom includ- 

 ing rudder movements) must be analyzed in evaluat- 

 ing a ship's trajectory. However it can be assumed that 

 analyses of moi'e limited groups, outlined in Sections 

 2.33(a) and 2.33(6), will provitle useful results. The 

 author doubts that a solution of equations of motion 

 with constant coefficients is realistic in connection with 

 roll-pitch-yaw motions of a ship in ([uartering seas, and 

 suggests a step-bv-step integration of e([uations with 

 variable coefficients. The coefficients of the ec{uations 

 can be found in the way used by Kor\'in-Kroukovsk;y 

 and Jacobs (1957) for pitching and hea\ing. Evalua- 

 tion of some of the coefficients is less certain at present 

 in the case of unsymmetric motions; nevertheless, the 

 available material is believed to be sufficient to justify 

 the project. It should be understood that some of the 

 coefficients may be evaluated on the basis of model test 

 data, and that the first attempt necessarily will be semi- 

 empirical. 



The use of digital computing machines was visualized 

 for the solution of the differential er|uations. However, 

 analog computers capable of analyzing motions with 

 many degrees f)f freedom ha\'e been de\'eloped for con- 

 trolled aerial missiles. Setting up a similar facility for 

 the study of .seven-degrees-of-freedom ship motions in 

 irregular seas is recommended. 



7.2 Observations on Ships at Sea. For many years 

 investigators of ship motions thought in terms of simple 

 harmonic or simple trochoidal wa\es, as representing the 

 average effect of irregular sea conditions. The irregular- 

 ity of the sea was well known ciualitatively, but the sig- 

 nificance of this irregularitj' for ship motions was not 

 sufficiently realized. The technique of quantitative 

 treatment of irregular sea and ship motions is barely 

 7 years old and further development is expected. Never- 

 theless, it can now be considered as established. Its 

 broad application, however, is handicapped (a) by 

 difficulty in following the current literature on the sub- 

 ject and (b) by the scarcity of electromechanical ana- 

 lyzing equipment. 



Regarding the first item, it should be realized that 

 knowledge of the effects of irregular seas cannot be lim- 

 ited to a few specialists. It is essential that all towing- 

 tank technicians, naval architects and mariners have 

 sufficient understanding of it. These men are fully 



occupied in their professions and cannot be asked to 

 study books on statistics in which only a small per- 

 centage of the contents applies to the present problem. 

 The author considers it essential, therefore, that simple 

 texts be prejiarcd in order to present the irregular sea 

 theory and its application with a minimum of spe- 

 cialized statistical termiijology. 



The analyses needed in connection with irregular seas 

 can be made on digital computing machines or on elec- 

 tronic filtering machines. The use of digital computing 

 machines requires reading the record tapes, and doing 

 this manually is too tedious to permit widespread use of 

 the analysis. The digital computers must be supple- 

 mented by curve-reading machines for rapid conver- 

 sion of tape records into typed tables. Or, better yet, 

 the tabulating device should be made a part of the re- 

 cording equipment. At best, however, the use of digital 

 machines leaves a wide time gap between obtaining the 

 information and getting the results analyzed. This 

 procedure can be considered, therefore, onlj' as a stop- 

 gap, pending the development of special analyzers. 



An analyzer operating on the principle of electronic 

 freciuency filtering may gi\e the results of an analysis 

 in a few minutes after the record is taken. The author 

 considers this feature vital in efficient towing-tank op- 

 erations and in observations at sea. The investigator 

 should obtain the analyzed data while the observed be- 

 havior of a ship or a model is fresh in his mind. This 

 should facilitate greatly the interpretation of events and 

 should speed up final conclusions. It also will help to 

 decide the next step in towing-tank experiments. At 

 sea it may help to determine the success of a certain test 

 maneuver. The development of simple portable elec- 

 tromechanical analyzers, capalile f)f spectral and cross- 

 spectral analyses, is recommended. It is desirable that 

 they also give the autocorrelation functions, which are 

 neces.sary for certain analyses and are particularly valu- 

 able in indicating the presence of harmonic (nonrandom) 

 oscillations. 



The need for development of such e(iuipment in towing 

 tanks will become acute as the use of irregular wa\'es 

 widens. The author has expres.sed his belief. Section 

 4.41, that the use (jf irregular waves is neces.sary lor 

 model testing in oblique waves. 



Observations on ships at sea are now entering a new 

 era with the a\-ailability of ship-borne wave recorders 

 and development of the statistical theory of irregular 

 waves. These two must be considered together. At 

 present, Tucker's (1-19526, 1956) recorder appears to 

 be the most practical device. However, the wave in- 

 dicators used on the MS iSV;« Francisco and SS Ocean 

 Vulcan would have been capalde of giving the same 

 valuable information if the measurements were made 

 and analyzed in the light of the new theory. 



In addition to a wind-sea, swells almost always are 

 present in the North Atlantic. Ship motions probably 

 are affected more freciuently by swells than by the wind- 

 sea, and, therefore, both should be ob.served and re- 

 corded. However, it becomes impossible to distinguish 



