Paii-doussis 



-\ 1 1 — I I I I I I 1 1 1 I I M I I 1 1 1 1 I I I I I V- 



OSCILLATIONS 



YAWING 



' ' ■ ■ ■ I 



10 



-I 1 — I I I ^ V" 



50 100 1000 



A 



Fig. 15, The effect of A on stability of a rigid cylinder 

 with f,= i-C| = l, eCf^=ecj=0,5, C2=i-f2 

 and X| =X2 = 0»01« (Theory of [ 26] ). 



the tow-rope length. In the case of the rigid body this becomes 

 obvious upon considering equation (19). Since the threshold for 

 yawing instability implies co = 0, this threshold is established by 

 the equation E = 0. Now E is foxond to be 



E= (c^p/2A)[|€(c^ + c^) - Zf^]. 



Clearly we see that the threshold is not dependent on A. This seems 

 to be in contradiction with Strandhagen's et al. [l ] criterion (iii) for 

 the stability of towed ships (as given in §1); on closer examination 

 of their own work, however, we see that the equivalent of term E, 

 in their case also, contains A as a common factor. Accordingly, 

 we must conclude that the only form of instability the existence or 

 non-existence of which may be controlled by the tow-rope length is 

 oscillatory. 



6,3 Ccilculations Based on the New Theory 



Calculations were also conducted with the new theory. It was 

 found that, in this case also, the dynamical behavior of the rigid 

 body corresponds to that of the zeroth and first modes of the flexible 

 one at low towing speeds -- quantitative correspondence of frequencies 

 occurring at u = l/v2 as before. 



Stability plots were also constructed (Figs. 16 and 17). These 

 are markedly different to those given by the old theory (Figs. 14 and 

 15) , the main difference being in that oscillatory instability according 



1008 



