Woterline 



Ship 



Figure 1 - Dimensions and Forces on an Anchor Cable 



Here D is the horizontal component of tension in the anchor line at the ship (drag of 

 the ship), in pounds, 

 L is the vertical component of tension in the anchor line at the ship, in pounds, 

 T = VL'l + D't, the tension in the anchor cable at the ship, in pounds, 

 T = T - WY, the tension in the anchor cable at the anchor, in pounds, 

 W is the weight per unit length of the anchor cable in water, in pounds per foot, 



Y is the depth of the water, in feet, 



^0 is the angle of the anchor line with the horizontal at the anchor, in degrees, 

 M = R/w, the current parameter, 



R is the drag per unit length of the anchor cable, 0.34- V 2 d for wire rope and 0.20 

 V^h for chain, 



V is the current speed, in knots, 



d is the diameter of the wire rope, in inches, 



h is the outside width of a link of chain, in inches, and 



S is the length of the anchor line, in feet. 



of the hydrodynamic force on the line is neglected in these computations, but 

 the resulting error is partly offset by the assumption that the velocity of 

 the current is the same at all depths; actually the current velocity is known 

 to approach zero rapidly near the bottom. 



Figures 2, 3, 4, and 5 are polar diagrams of the vertical and hori- 

 zontal components of the cable tension at the waterline, expressed as dimen- 

 sionless quantities in terms of the weight WY in water of a length of anchor 

 line equal to the depth. Plots of this type are called polar diagrams be- 

 cause the polar coordinates, i.e., the radius from the origin and the angle 

 of the radius with the D/WY axis, give the magnitude of the tension and the 

 inclination of the anchor cable with the horizontal at the ship. 



In anchoring a ship it is considered desirable to pay out enough 

 line to permit the cable to be horizontal at the anchor. The reason for this 

 is that the holding power of an anchor falls off linearly with the angle of 

 inclination of the cable at the anchor; the holding power is reduced by one- 

 half for an angle of 30 degrees with the horizontal, as shown in Figure 13 

 of Reference (3). Consequently, it is desirable to have a method for esti- 

 mating the length of line needed to ensure that the cable will be horizontal 

 at the anchor. Figure 2 was devised for this purpose. 



