b. Increasing length of chain pendant/bridle
c. Inserting a synthetic spring into the towline system.
The following explores the ability of a wire catenary to absorb ship movements by including "stretch" of the wire. From
paragraph 5-4.4 the depth of a tow hawser catenary can be estimated by the formula:
C = T/W - T/W √ 1-(WS/2T)2
If the effects of hydrodynamic drag are ignored, catenary theory further estimates the separation between tug and tow as:
D = S(1-WC/3T)
Catenary depth or sag (ft)
Steady tension in the towline (lbs force)
Weight in water per unit length of the hawser (lbs/ft)
Total scope of the hawser (ft)
Horizontal distance between the tug stern and the bow of the tow (ft)
See Figure 5-2 for a graphical representation of the notation used.
In order to quantify the effect on the hawser tension for a given change in distance between tug in tow, it is necessary to
develop a table or curve of distance (D) vs. tension (T) for various hawser scopes. The computation is fairly direct if
tension (T) is assumed for a given scope (S) of hawser, catenary depth (C) is computed, then horizontal distance (D) of
Two components of wire "stretch" must also be included: constructional stretch and elastic stretch The Wire Rope Users
Manual (Ref. 13) estimates constructional stretch as 1/2-3/4percent for 6-strand fiber-core wire and '1/4-1/2, percent for
6-strand IWRC wire. It can be assumed that constructional stretch is linear up to a load of about 20 percent of breaking
strength, beyond which there is no additional constructional stretch.
The elastic stretch of hawsers likewise varies with load. For convenience, elasticity is assumed to be constant through
20 percent loading, with a different figure applying beyond 20 percent loading For common Navy hawsers, the following
figures can be used, expressed as section modulus in feet stretch, per pound load, per foot of length'
(multiply all values times 106)
Example: A 1,000-foot, 2-inch FC hawser with a 20,000-pound load will elastically stretch
20,000 x 1,000/16.6 x 106 = 1.2 ft.
Table 6-2 is developed for a 1,000-foot, 2-inch, FC hawser, with the results plotted in Figure 6-13 An 1,800-foot hawser
of the same material is also plotted for comparison. Ships with different hawsers can prepare a family of curves showing
the change in tension as the separation between the ships changes For instance, from an initial tension of 20,000
pounds, the 1,000-foot hawser can absorb about 19 feet of additional separation between the tug and tow before it
reaches 200,000 pounds tension; the