is parallel to the cylinder axis, and this connponent depends in space only 

 on the distance r from the axis. 



A tangential (axial) stress on the cylinder surface is given by 



9w 

 ¥7 



Wnb 



p Ny CO 



- ^0° / 



V cos I 



Got + e + p - Y + 



37r\ 

 4 / 



where b, c, P, "y are real numbers defined by 



be = ker, "v — a + ikei, v — a 



i V 1 V 



c e - ker 



— a + i kei N/ — a 



Thus there is an axial force component per unit length on the cylinder: 



F = - 



2 TT p a \' ojv Wq b 



cos(wt+€+P-\ + 



3£\ 



4 / 



2 TT p a \l Lov Wq b 



cos(cot+e)coslp-Y+ — I 



Ln(wt + sin^p - V + — ) I 



The first term in brackets in the last equation gives the drag force. 



For the slender bodies considered in this report, it is consistent to 

 calculate the viscous force in a strip^vise manner. That is, at each cross 

 section of the i spar, where the radius of the section is a- (z-'), we con- 

 sider that particular section to be part of an infinitely long right circular 

 cylinder translating axially, calculate the axial viscous force per unit 

 length, and integrate such results over the length of the spar. To first 

 order in the naotion variables, the axial velocity of the i spar is 



Zq + a^fa sin 9- - P cos 6.) 



27 



