-5 2 

 Now, for water v = 1.1x10 ft /sec. Therefore, for a and t« 



/ UJ 

 even as small as 1 inch and 0.16 rad/sec, respectively, a / - » 1 and the 



Hankel functions can be expanded asymptotically. Then 





(A-4) 



Therefore, 



. TT 



F = -2tt ap >/uJv" W e ^4 (A-5) 



This equation shows that the viscous force is out of phase with the velocity of the 

 cable . 



Thus, it has been shown that the viscous damping on the cable is pro- 

 the veloci 

 is obviously given by: 



portional to the velocity of the cable. The coefficient 3 used in Section IV-A 



Now for a metallic cable p s: 500 Ib/ft^ and c ^ 12,000 ft/sec. Thus, with 



c 



the values of p and v for water and L and a equal to 20, 000 feet and 1 . 125 



inches, I I = 0.013 uJ' *. For smaller L, I 8 I is even smaller, and it is 



' c c 



hardly possible to have a of a smaller order of magnitude than 1.125 inches. 

 The inertial term in Equation 7 is of order m , while the friction term is of 



order U)' I 3 I = 0.013 uj'^/-^. Therefore, for m' s 0.02 the friction term can 



' c' 



be neglected as compared to the inertial term (except at very sharp resonances). 



33 



artbuT Jl.HittleJnt. 



S-7001-0307 



