The second approximation of the free surface elevation is given by 



1 I *, HA 



Y 3$ 



1 Y l 



q o 3C ' c=o 



Therefore, the free wave pattern at far downstream becomes 



tt/2 

 -it/ 2 



(83) 



J 



, , , i sec (C+H tan 0) 3 Q . ,,,,, 

 C, ss - Re A(0) e sec 6d0 (84) 



because q_ *? 1 at a great distance. 



The wave resistance experienced by the ship is derived from momentum 

 or energy analysis of free waves at a great distance. It is determined by 

 the amplitude function 



tt/2 



n TT 2 ,2 I 



w 2 



I 



R =|pU 2 A 2 |A(0)| 2 sec 3 0d0 (85) 



-tt/2 



In order to calculate A(0) , we need the inverse transform of Equations (69) 

 and (70) . For this purpose, we take curvilinear coordinates along 

 streamlines and equipotential lines along which the length s and t are 

 taken, respectively. It is proved that we have the relations 



34 



