Vassilopoulos and Mandel 



the total exciting force due to sinusoidal waves is simply obtained by summing 

 up the individual contributions of each strip, i.e., 



+L/2 /32^ 



"d7 



-L/2 



Zg(h,h,h, t) 

 and the total pitching moment is given by 



Me(h,h,h,t) = J (^j 



-L/2 



dx = Z„ e 



(38) 



X dx = M_ e 



(39) 



It is interesting to compare the above expressions with those of Jacobs [14]. 

 Following the same initial steps as Korvin-Kroukovsky [10] but pursuing a 

 slightly different approach, Jacobs [14] modified and improved the excitation 

 force expression as compared with the one given in Ref. [10]. In our notation, 

 the formula as given by Jacobs [5] and as used in the existing computer program, 

 reads as follows: 



dZ„ 



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



N(x) - u. 



d^x) 



dx 



h(x, t) + iJ.(x) h(x, t) 



X exp 



277 



a(x) H(x) 



(40) 



Equation (40) differs from (37) 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 dis- 

 cussed 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. 



As justification of using the cross-flow hypothesis in computing excitation 

 loads. Fay [13] provides an intuitive criterion which requires that 



> 1 . 



The best criteria however of the success with which strip theory predicts the 

 forcing function is the degree of correlation with experimental measurements 

 and more sophisticated theoretical analyses. As far as the authors are aware, 

 the only experimental data obtained with actual ship models is that of Jinnaka 

 [48], Schultz [49], and Gerritsma [22], whereas Gersten [50] and Lee [51] meas- 

 ured excitation forces and moments on mathematically defined bodies. Corre- 

 lation between experimentally measured and theoretically computed exciting 

 forces and moments have been presented by Vossers [47], Gersten [50], and 

 Lee [51], but the theoretical expressions used for the exciting loads differed 



342 



