10 



assumed sizes of cable. The optimum solution is the size of cable which will 

 be loaded up to the safe working load under the given conditions. 



EXAMPLE 



Consider a ship whose displacement is 2000 tons, whose length is 360 

 feet, and whose beam is 40 feet, anchored in water 300 fathoms deep. Assume 

 a 4-knot tide and a 70-knot wind, both in the same direction. It is desired 

 to find the diameter and length of a wire-rope anchor cable and the size of 

 anchor required. From Equation [2], the drag of the ship is 



D = 0.0022 x (40) 2 x 4900 + 0.12 x 16 V360 x 2000 

 = 17,200 + 1630 = 18,830 pounds 



The forces on the anchor will be examined for cable diameters of 1 , 

 1.5, 2, and 2.5 inches. For convenience in the subsequent calculation, the 

 values of W, WY, n, and D/WY for these diameters and for Y = 1800 feet have 

 been computed from Equations [4a] and [5a] and assembled in Table 1. From 

 Equations [6a] and [7a] the values of T B /WYand T a /WY are found to be 27.8 

 and 8.89 respectively for all diameters. 



TABLE 1 

 Values of W, WY, n, and ^ 



d 



inches 



W 



pounds 

 per foot 



WY 

 pounds 



V 



D 

 WY 



1.0 



1.5 



2.0 



2.5 



1 .40 



3.15 

 5.60 



8.75 



2,520 



5,670 



10,080 



15,740 



3.84 

 2.56 

 1.92 

 1.54 



7.47 

 3.32 

 1.87 

 1 .20 



Figure 6 illustrates the procedure for d = 1 inch and S/Y = 3, i.e., 

 for the chart of Figure 4. The point corresponding to n = 3.84 and D/WY= 

 7.47 is spotted on the chart. The values of L/WY '= 5.4 and <j> = 7-0 degrees 

 are then read by interpolation. The length of the radius vector to the point 

 is readily obtained by swinging an arc with center at the origin back to the 

 D/WY axis and reading the value at the intersection of the arc with this axis. 

 This gives T/WY= 9.25 and then, from Equation [la], T = 20,800 pounds. The 

 circle of safe working loads with radius T,/WY= 8.89 is also shown in Figure 

 6. The factor of safety, T B /T, is computed as the ratio of T B /WY to T/WY 

 where 



