A New Appraisal of Strip Theory 



a. a factor of 2 appears in the velocity dependent terms of eCw^) and B(oj^), 

 and 



b. a pseudo-three-dimensional term is introduced in coefficients e(Wg), 



B(co^), c and E(co^). 



"It would also appear that the introduction of terms dependent on the rate of 

 change of added mass over the ship length is inconsistent with the use of two- 

 dimensional theory. Despite these discrepancies, however, it is expected that 

 the final values of these coefficients will not be seriously modified since it has 

 been shown by Jacobs et al [5] that most of these terms which appear in the 

 Korvin-Kroukovsky approach but not in the new approach are numerically small. 

 It is hoped that in the near future these inconsistencies will be examined more 

 carefully and their implications assessed on the basis of experimental data." 



Several pages later you say ". . . In our notation, the formula [for the exci- 

 tation force] as given by Jacobs [5] and as used in the existing computer pro- 

 gram [at M.I.T.], reads as follows: 



-^ = ^ pgB(x) h(x,t) + 



exp 



N«-u„^ 



^Cr(x) H(X) 



h(x, t) + /^(x) h(x, t) 



(40) 



Equation (40) differs from (37) [the new approach] in that the wave velocity term 

 includes an extra pseudo-three-dimensional term which is furthermore speed 

 dependent. The contribution of the latter term is small in comparison with the 

 other terms and predicts a decrease of the exciting force and moment, a finding 

 which, as discussed by Vossers [47], contradicts that of Hanaoka. It is contended 

 that the more rationally derived Eq. (37) will give almost similar results as 

 Eq. (40) but this remains to be verified." 



I should like to take up a few points. 



1. It appears to me that this criticism boils down to one ingredient: we dif- 

 ferentiated a "fixed" coordinate i with respect to time and hence inevitably the 

 "fixed" radius r of the circular section associated with f . The latter deriva- 

 tive 



dr _ dr d^ _ _ „ dr 

 dt " dj dt " ~ dj 



would then give terms, dependent on a rate of change of r (and hence of added 

 mass) over the ship length, and also speed-dependent. 



In our approach, the ^-axis fixed in the ship is time-dependent with respect 

 to the wave. Our strip method treated each ship section strip as if fixed in a 

 frame of an animated cartoon with the strips changing from frame to frame and 

 the frames changing from time to time. 



357 



