Vassilopoulos and Mandel 



These are the three coefficients which are different from yours. The difference 

 is negligible in the case of BC^^) and small in the case of c. However, the sec- 

 ond term of E is of the same order of magnitude as the first term. 



The reason for not substituting 



- t fi(x)dx for r ^ti^ xdx 



in our definitions of the coefficients is that the unit force and moment coeffi- 

 cients are required in the computations of bending moments. 



3. You criticize the Jacobs formula for unit exciting force, given in your 

 Eq. (40), because the coefficient of the damping component contains, in addition 

 to NCx), a term 



a "pseudo-three-dimensional" term which predicts a decrease of the exciting 

 force and moment as forward speed u^ increases, whereas Hanaoka's calcula- 

 tions, as shown in Vossers' articles, predict an increase. This criticism would 

 be valid only if the damping coefficient N(x) were invariable with forward speed. 

 However, N(x) is a function of speed through its dependence on frequency of en- 

 counter, and itself contributes to the decrease in exciting force with speed. As 

 you say, the contribution of the disputed term is small and your Eq. (37) which 

 omits this term "will give almost similar results as Eq. (40) but this remains 

 to be verified." 



4. But why not verify it? Since the computer program at M.I.T. follows the 

 computational procedure of Davidson Laboratory Report 791, it should be quite 

 easy to drop the offending terms and test your new approach. 



K the Korvin-Kroukovsky approach is devoid of vitality, why keep flogging 

 a dead horse ? 



DISCUSSION 



Martin A. Abkowitz 



Massachusetts Institute of Technology 



Cambridge, Massachusetts 



I should like to discuss specifically the nature of the various coefficients in 

 the coupled linearized equations of motion for pitch and heave as tabulated in 

 Table 2 of the paper. 



360 



