A New Appraisal of Strip Theory 



mass were assumed by Korvin-Kroukovsky [10] and Jacobs et al. [5] to apply to 

 more general cylinders. However, different results were used in Refs. [10] and 

 [5] for computing the damping coefficients; the first utilized an approximate ex- 

 pression for A, whereas the second introduced and employed the graphical data 

 computed by Grim in 1953 [29]. Since the publication of Ref. [30] which reviewed 

 the state of art up to about 1955, the important problem of the oscillating cylin- 

 der of arbitrary section has been examined and solved in greater detail, both 

 theoretically and experimentally. For example, Grim [29], Tasai [31] and, more 

 recently Porter [32] have extended the Ursell problem to more general cylin- 

 ders, and have provided added mass and damping as a function of the frequency 

 of oscillation. Damping coefficients for extreme V sections were also evaluated 

 by Kaplan [33] using a Green's function technique, whereas TRG [34] presented 

 their approximate method for evaluating these quantities. These theoretical 

 studies were supplemented and verified by experimental work carried out by 

 Tasai [31], Porter [32], and PauUing and Richardson [36] and Watson [35]. 



These studies were of course concerned with the small oscillatory motion 

 of two-dimensional bodies where the effect of frequency on the distribution of 

 damping and added mass, the effect of forward speed, and nonlinear effects are 

 ignored. These important effects have been discussed on the basis of experi- 

 ment in part by Golovato [37] and in part by Gerritsma [38], and Gerritsma and 

 Beukelman [39] and others. Reference [39] has shown for example that the dis- 

 tribution of damping along the length of a ship is appreciably affected by fre- 

 quency and forward speed whereas the added mass distribution appears to be 

 less affected by these parameters. Another very important point, which was 

 anticipated from Newman's theoretical work [40] was the occurrence of negative 

 sectional damping and added mass at certain speeds. Two-dimensional theory 

 cannot of course predict such effects. Hence, strip theory fails to compute ex- 

 actly the responses but more especially the bending moments in regular waves. 



The computer program described and used in Ref. [6] made use of a sub- 

 routine which was based on more recent work by Grim, as outlined in Ref. [41]. 

 His numerical results however appeared to be erroneous for certain combina- 

 tions of sectional area coefficient and beam-to-draft ratio. This issue assumed 

 great importance when disagreement was noted in the case of Model E as dis- 

 cussed earlier in this paper. Furthermore, his results, as well as those of 

 Tasai [31], are restricted to Lewis shape sections only. However, as far back 

 as 1947, Prohaska [42] indicated that the definition of a ship section in terms of 

 two parameters is unsufficient. This inadequacy has since been clearly demon- 

 strated by Landweber and Macagno [43], in connection with high-frequency added 

 mass calculations. 



The above points and the availability of a complete and exact analysis of the 

 problem by Porter [32], launched a systematic examination of the problem which 

 is currently still under way at M.I.T. by Porter and others. Some preliminary 

 results of this work are herein included and discussed. Comparison of k^ and 

 A as calculated by two computer programs, one based on Grim [41] and another 

 due to Porter [32], are shown in (a) Figs. 66 and 67 for semicircular cylinders 

 of varying beam to draft ratio and, (b) Figs. 69 and 70 for the typical ship sec- 

 tions illustrated in Fig. 68. The latter figure and Table 3 are reproduced from 

 Ref. [44]. 



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