A New Appraisal of Strip Theory 



relationship between the wave-induced force on a fixed body and the amplitude 

 of the progressive wave caused by the motion of the body in still water. Al- 

 though his analysis does not provide the phase between force and wave, his ex- 

 pressions ought to be compared and evaluated on the basis of strip techniques. 

 Using our notation, it can be shown that for a ship hull, his final formulations 

 reduce to: 



2 ^+L/ 2 



(41) 



(^) I 



Z. = P (tM I A(x) h(x)dx 



J 2 



and 



2 p+L/2 _ 



M„ = P (^) J A(x) h(x)xdx. (42) 



Finally, three-dimensional corrections deserve comment. The work of 

 Spens [53] and others has suggested that a three-dimensional correction to al- 

 low for end effects, etc., tends to worsen agreement between theory and experi- 

 ment. Further analysis on this point is needed, however, because there is re- 

 cent experimental evidence at M.I.T. to suggest that neglect of three-dimensional 

 effects may not be in order for certain ship forms. Provided that the other 

 neglected effects are allowed for, it may well be that a three-dimensional cor- 

 rection will improve agreement between theory and experiment. 



CONCLUSIONS 



1. Following Abkowitz [12,26,27], the more rigorous development of the 

 equations of motion shown in this report along with the more systematic and 

 symbolic notation of the SNAME Bulletin 1-5 [25] lead more quickly and simply 

 to an accurate definition of the various parts of tiie coefficients of the equations 

 of motion than the Korvin-Kroukovsky approach. 



2. The quantitative evaluation of the coefficients of the equations of motion 

 using strip theory developed in this report leads to agreement with Korvin- 

 Kroukovsky in the case of eight of the coefficients and disagreement in the case 

 of four of tile coefficients. 



3. Figures 2-65 show that pitching and heaving amplitudes as well as phase 

 aisles as computed by Korvin-Kroukovsky' s procedure using Grim's section 

 damping and added mass [41] correlate reasonably well with existing experimen- 

 tal data which however also include sources of possible error. 



4. Substitution of the Porter method [32] for computing section damping and 

 added mass should improve the discrimination amongst differing section shapes 

 compared to Grim [41] and also removes the difficulties associated with oscil- 

 lating nature of Grim's coefficients shown in Figs. 66, 67 and 69. 



5. While it has been hypothesized that the correlation shown in Figs. 2-65 

 may be due to fortunate cancellation of substantial errors, it is not believed that 



345 



