178 



THEORY OF SEAKEEPING 



lished only in the broadest sense of a mean order of mag- 

 nitude and of tendency to maximum at synchronism. 



3.71 Work of Voznessensky and Firsoff. In the pre- 

 ceding sections, a particular ship's resijonse to a specifi- 

 cally defined seaway was discussed, ^'oz^essensky and 

 Firsoff (1957) on the other hand, treated typical forms of 

 seaway and the rolling responses of typical ships, ^'oz- 

 nessenskj- and Firsoff 's definition of the sea spectrum was 

 discussed in Section 1-6.6. The form of scalar wave 

 energy sj^ectrum was defined by two parameters a and (3 

 as a function of the total spectrum area or, in other words, 

 in terms of the significant wave height. Tlie frecjuency- 

 response function in rolling was taken to be that of a 

 simple harmonic oscillator in terms of the damping coef- 

 ficient anil the ship's natural freijuency in roll. To equa- 

 tion (2o) was applied a corrective factor which took into 

 account short-crest edness of the sea and also the reduct- 

 tion of the true fre(|uency-response function in very short 

 waves. Formulas and curves were given for estimating 

 all factors needed for computations. Finally a ship's 

 i-olling amplitude in waves of a specified significant height 

 was predicted. Application to six ships showed this pre- 

 diction to hold within 25 per cent of the observed value. 

 The main cause of the differences is the \ariability of the 

 sea form (i.e., variability of parameters a. and ^) within 

 a given significant wave-height specification. 



The ]3articular \-alue of ^'oznessensky and Firsoff's 

 (1957) paper appears to lie in its presentation of a very 

 large amount of sea data obtained by instrumentation 

 and in the classification of the data in terms of two 

 parameters as a function of the significant wave height. 

 Another valuable step is the introduction of a correction 

 factor for transition from an idealized scalar spectrum to 

 the true sea conditions. 



The shortcomings of the method lie in failure to con- 

 nect the .':ea state parameters a and (3 with wind condition 

 and in the uniformity of the characteristics of all ships 

 used in the analysis. 



The latter remark can be amplified by a historical 

 sketch. At the beginning of the steamship era, ships 

 were built with excessive metacentric height and verj^ 

 short rolling period. Possibly an extreme example is the 

 SS Great Eastern with its displacement of 22,500 tons and 

 rolling period of 6 sec (Dugan, 1953; Wm. Froude, 1861). 

 Ships of this type would roll hea\ily when ho\-e-t() head- 

 on in a storm. Later, the ad\-antages of a low metacen- 

 tric height and a long rolling period (up to 20 sec) were 

 demonstrated, both theoretically and by sea observations 

 (Wm. Froude 1861; Mockel, 1941). Rolling of ships of 

 this kind was treated by Manning (1942), and it was 

 found that the most critical condition occurred in quar- 

 tering seas. Lately, there has been a tendency to in- 

 crease the metacentric height and shorten the rolling 

 period. A rolling period of about 12 sec has become 

 typical for ships of 60 to 70 ft beam. These ships roll 

 most hea\'ily in a sea from approximatelj^ beam direc- 

 tion. \'oznessensky and Firsoff's treatment was limited 

 to these conditions. 



The loading of cargo ships, however, varies widely and 



excessively short periods of rolling are freciuently en- 

 countered (Patterson, 1955). Investigations of ship 

 rolling should not be limited, therefore, to beam seas but 

 should aim at miiversality. 



4 Model Tests in Waves 



Many towing tanks were equipped at an early date with 

 de\'ices for generating regular waves. Mf)del experi- 

 ments in waves were conducted by R. E. Froude (1905), 

 Kent (1922, 1926), Kempf (1934, 1936) and many others. 

 Since only long narrow tanks were available, tests were 

 limited to head or following regular waves. Kent also 

 ex]5erimented with an irregular sea generated by manu- 

 ally changing the wave-maker speed, without specifically 

 defining the nature of the resultant irregularity. 



For a long time no attempt was made to compare the 

 test results of various tanks. The need for such a com- 

 parison was finally realized, and a program for action was 

 devised at the Sixth International Towing Tank Con- 

 ference in Washington in 1951. Results of the experi- 

 ments in the various tanks on a model of the series 60, 

 O.GO block coefficient hull were collected and reported by 

 \'edeler (lU55c) at the Seventh International Conference 

 on Ship Hydrodynamics in Norway, Denmark and 

 Sweden. The data obtained in the different towing tanks 

 for regular iiead waves demonstrated very poor agree- 

 ment in amjjlitude of pitching motions and sometimes 

 e\'en in the fretiuency at which synchronism was ob- 

 tained. Subsequently, a task group was formed under 

 the auspices of the Seakeeping C'haracteristics Panel of 

 Hydrodynamics Committee of The Society of Naval 

 Architects and Marine Engineers in order to organize a 

 new series of comparative tests in small tanks in the 

 United States. Again a series 60, 0.60 block coefficient 

 model was used, one 5 ft long. The results of these tests 

 were reported by Abkowitz (1956a, 1957f/) at the Elev- 

 enth American Towing Tank Conference and at the 

 Eighth International Towing Tank Conference in Ma- 

 drid. A satisfactoiy degree of agreement among the four 

 participating tanks was obtained at higher speeds.'^ 

 The comparison included amplitudes of heaving as well 

 as of pitching. The most important sources of previ- 

 ously encountered discrepancies were found to be the ir- 

 regularity and uncertainty of the wave amplitude and the 

 lack of precision in recording the data. The improved 

 agreement, compared to the poor international one, re- 

 sulted from improved wave generation, improved wave- 

 height recording and because the results were referred to 

 the wa\'e height actually measured rather than to the 

 nominal, specified wa\'e. The recording apparatuses also 

 were improved, and more painstaking care was used in 

 conducting the experiments. 



At lower speeds (roughly below 1.5 fps for a 5-ft model) 

 the data appear to lie afl'ected by wave reflections from 

 tank walls. Comparative tests in a conventional narrow 

 tank and a newly available wide tank are plaimed. 



" At speeds above the synchronous one in wave length equal to 

 ship length. 



