Dynamios of Submerged Towed Cylinders 



(O 



ifi) 



(c) 



Fig. 9 Photographs in consecutive frames showing a cylinder 



15,8 in. long and 0,68 in. diameter executing (a) criss- 

 crossing, essentially rigid-body, oscillation (8 frames/sec), 

 (b) second-mode flexural oscillation (24 frames/sec), 

 and (c) third-mode flexural oscillation (Z4 frames/sec) 



Figures 10 and 11 show the dynamical behavior, with in- 

 creasing towing speed, of the zeroth, first, second and third modes 

 of a system with well streamlined nose and tail and A = 1; this Is 

 the identical system, the dynamical behavior of which, according to 

 the 'old' theory, is shown in Figs. 3 and 4. We observe that, accord- 

 ing to the new theory, the system is considerably more stable than 

 predicted by the old theory. Thus, the first mode is unstable only 

 for u < 0.74 (not discernible in the scale of Fig, 10); moreover, 

 the unstable locus originating from merging of branches of the 

 zeroth and first modes regains stability at u = 6.3. Similarly, the 

 system loses stability in its second and third modes at respectively 

 higher towing speeds than predicted by the old theory. 



Further calculations were conducted for the same system as 

 above but with other values of £2' always taking Cg = 1 - fp* It was 

 found that the first mode is not uniformly stabilized with decreasing 

 f 2 as was the case with the old theory (cf. Fig. 6). The ranges of 

 instability of the first mode, for various values of f2, were found 

 to be as follows: < u < 0. 74 for f2=l; 0<u< 1.66 for f2=0.8; 

 < u < 1.65 for fg = 0.6; and < u < 0. 70 for fg = 0,4. Thus the 



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