DYNAMICS OF SUBMERGED TOWED CYLINDERS 



M, P. Pa'idoussis 



MaGill University 

 Montreal J P.Q.j Canada 



I, INTRODUCTION 



Interest in the dynamic stability of towed ships dates back to 

 the halcyon-days when solutions to engineering problems could still 

 be obtained by experience, without the aid of sophisticated analysis. 

 Certainly, operators of horse-drawn barges in canals must have 

 been aware of possible instabilities and remedial actions. Never- 

 theless, to the author's knowledge, the first substantive paper on 

 the subject, by Strandhagen, Schoenherr and Kobayashi [ l] , did not 

 appear until 1950. This is also surprising, if one considers that 

 both the analytical techniques and physical concepts were understood 

 long before that; indeed much earlier work does exist on the closely 

 related topic of stability of airships moored to a mast and kite bal- 

 loons, starting with the work of Bairstow, Relf and Jones [ 2] in 1915, 

 and followed by the work of Munk [ 3] , Glauert [ 4] , and Bryant, 

 Brown and Sweeting [ 5] , for Instance. 



Strandhagen et al. , and the discussors of their paper, firmly 

 established the following important criteria for stability of a towed 

 ship: (i) the point of attachment of the tow-rope should be ahead of 

 both the center of mass and the center of pressure of the (static) 

 lateral hydrodynamic forces acting on the ship; (il) the ship should be 

 stable when moving untowed; (iii) in cases where (ii) is not satisfied, 

 then the system could be rendered stable by either short enough or 

 long enough tow-ropes. It is noteworthy that the criteria for stability, 

 at least for the linearized theory of small departures from course, 

 apply to all towing speeds, so that for a given configuration a (rigid) 

 towed ship is either stable or unstable irrespective of how fast it is 

 being towed. Instabilities were found to be of two distinct types: 

 (a) yawing, i.e. a zero-frequency, amplified motion which in aero- 

 elasticity would be referred to as 'divergence', and (b) oscillatory 

 instability, where the system, when disturbed, oscillates about its 

 position of rest with increasing amplitude. 



More recently, interest in the instability of submerged towed 

 bodies has arisen nnainly in connection with sonar applications. Here 



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