1194 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



Air: 



2rr e'^</EA 

 e T2 = 



4Cif2 



. 2w.T , / , Ci . 2coL 

 r2 sin + I ^3 + — ^4 sill 



Ci \ C2 Ci 



Ci 2a)L\ 2a)a: , Ci 

 — — re cos I cos + — re 



Ci Ci I Ci C-i 



cos 2co^ + 



r3 sin 



r2 + — r4 cos + — re sm ) cos + — r4 



C2 Ci C2 Ci / Ci C2 . 



2coL 

 sin 2coi 





/ 2wa; 2coL\ f . 2icx . 2coL\ I F 

 rs I cos — cos ) — r2 1 sm — sm ) — ^—r 



Ci 



Ci 



Ci 



Ci 



Water: 



i^ _ eiJ'EA 



e 1 i 



4ciC2 



2coZ/ , . 2o}L 



— ri cos + rz sm 



Cl 



, Cl . 2(joL I . 2u>Li 

 + — sm I r4 sm — re cos 



Ci C\ \ Cl Cl /_ 



sin 2: 



CO 



('-0 



+ 



. 2coL , 2(joL , Cl . 2a}L I . 2coL 

 r2 sin + r^ cos + — sin I re sm 



Cl Cl C2 Cl \ Cl 



+ r4 cos 



2coL 



Cl y 



COS 2u [ t — 



{■ - 9 



^|2C2^-2K 

 Cl J 



D.6 Numerical Results 



Since the r's are each proportional to the square of the amphtude A, 

 the above results indicate that the transverse motion tension varies as A 

 squared also. It is additionally a function of the frequency of ship motion 

 CO, the forward mean ship velocity V, and the stationary tension To . The 

 computation of the transverse ship motion tension for the laying situa- 

 tion was carried out for cable No. 2. The results are showii in Fig. 34. 

 Here we have denoted the transverse motion tension by Tq and have 

 plotted Tq/A^ against the period of ship motion t. Rather than the 

 stationary tension To , we have used the depth h, which during laying is 

 directly related to Tohy h = To/w. Fig. 34(a) is a plot of Tq/A~ versus 

 the period t = 27r/co for h = ^, 2 and 3 nautical miles and for V = 6 

 knots. Figure 34(b) is a plot of Tq/A^ versus t for F = 3, 6, and 9 knots 

 and h = one nautical mile. 



For representative laying, for example at 6 knots with a ship period 

 of 6 seconds into a depth of one nautical mile. Fig. 34 gives 



