14 



ILLUSTRATIVE EXAMPLE 



To provide an illustrative example of an application of the method, 

 the following problem has been worked out. 



It is desired to tow a body 25 feet deep at 30 knots. The body is 

 to have a lift-drag ratio of tan 70°. It is required that the safety factor 

 on the breaking strength of the cable be no less than 2. What is the minimum 

 size cable diameter that may be used, if the strongest wire-strand cable is 

 used? 



For such cable the following empirical data apply: Where d is the 

 cable diameter in inches and V is the speed in knots. 



•Cable drag normal to the stream: R •* 0.34 V 2 d pound per foot, 

 Cable drag parallel to the stream: F » 0.02 R, 

 Breaking strength of cable: S = 80,000 d 2 pounds. 



Since the safety factor must be no less than two, 4-0,000 d 2 ^ T; 

 where T is the greatest tension in the cable. Prom Table lb, for f = 0.02 

 and ^ = 70 we have the optimum value of T = (0.420 Ry). Hence 



d 2 £ 



;o.420)(0.34)(900)(25)d 



40,000 



d ^ 0.08 



The cable must therefore be at least 0.08 inch in diameter. Prom 

 Table lb it is seen that the jptimum length of this cable is (6.102)y or 525 

 feet. With this length of cable, the tension at ihe upper end of the cable 

 will be a minimum and equal to 2560 pounds. 



