Newman and Tuck 



« .8 



^ .6 



.2 .4 .6 .8 1.0 



Frequency in eye les per second 



Fig. 4 - Heave response calculated from first 

 order theory and compared with experimental 

 data at 0,14 Froude number 



all the familiar complications of damping, added mass, and the diffraction of the 

 incident wave system by the presence of the ship. 



The complete second order theory at zero speed is presented in Part II, 

 this work being an extension of the resvilts of Newman (1964), Figures 5 and 6 

 show the resulting pitch and heave response for the same conditions as Figs. 1 

 and 2, The first order theory and experimental data are repeated for compari- 

 son. It is apparent that there are only minor differences between the first- and 

 second-order results. 



At finite speed neither a complete theory nor calculated responses are as 

 yet available; the theory is presented in Part III for the case of forced oscilla- 

 tions only, leaving the exciting forces still to be determined. Thetheoretical 

 results of Part III (e.g., Eqs. 3.36) are presented in the form of double integrals 

 involving the cross-sectional area curve S(x) and/or the waterline beam curve 

 B(x) multiplied by a complicated kernel function K(x,w,U) where ^ is radian 

 frequency and u forward speed. If u = 0, K reduces as in Part II to a combina- 

 tion of Bessel and Struve functions which are tabulated; on the other hand for 

 non-zero u, K remains an vintabulated function defined at the moment only in the 

 form of a Fourier integral. More work is needed on investigation and tabu- 

 lation of this function before computation of responses at finite speed can be 

 carried out. 



136 



