whereas its drag increases with the square of the speed, the weight required 

 to obtain a given value of increases very rapidly with speed. Hence the 

 limitation on </> becomes more severe as the speed increases. The value of <j> 

 for a body employing lifting surfaces is not affected appreciably by speed or 

 by scaling its dimensions. However, the magnitude of the force obtained from 

 such a body varies as the square of the speed and as the square of the factor 

 to which its dimensions may be scaled. 



Let it be assumed that the direction of the force applied by the 

 body is known. The question is then how should the magnitude of the force be 

 adjusted. It is clear that if the magnitude of the force is very small, the 

 length of cable that is required will be exceedingly long so that the hydro- 

 dynamic force acting along the cable will cause the tension at the upper end 

 of cable to become very large. On the other hand the length of the cable is 

 shortest only when the magnitude of the force applied by the towed body grows 

 exceedingly large and then the tension in cable is also very large. Between 

 these extremes there must lie an optimum. 



ANALYSIS 

 The calculation of this optimum configuration depends upon the spe- 

 cific assumptions made regarding the forces acting on the cable. It can be 

 shown from very general considerations, however, that regardless of these spe- 

 cific assumptions the solution of the cable configuration can be expressed by 

 equations of the following parametric form. 



[1] 



[2] 



T 



T 





T o~ 



T o 





Rs 



a _ 



\ 



T o~ 



T 



c 



) 



Ry = 



V - 



''o 



T o 



T o 





Rx = 



t - 



*o 



T o _ 



T o 





[3] 



W 



where T is the tension at the upper end of the cable, 

 s is the length of the cable , 

 y is the depth of the body, 

 x is the distance of the body aft of the upper end of the cable, 



